While there are full methodological details below, the model I’ve developed is a full and thorough simulation of AV, modeling every round of transfers in all 650 constituencies, based on educated estimates of the transfer rates between different parties. I’ve run the model twice, under slightly different assumptions. In the first version of the model (which I’ll refer to as the simple model), I have assumed that the votes cast on the 6th of May would be the first preferences of voters in an AV election. This is a nice simple assumption to make, but it doesn’t take into account that people vote tactically in first-past-the-post (FPTP), and often won’t actually vote for their preferred candidate if they don’t think he has a chance of winning. AV would remove the incentive to do so, so you would expect that first preferences would be different than votes cast under FPTP.

In an attempt to account for this, I’ve also run a second version of the model (which I’ll call the adjusted model). One of the notable features of the recent election is how different the actual result was from what people were saying to pollsters right up to the day before the vote. It’s a reasonable hypothesis to say that the polls were reporting the actual preferences of voters, and that the shift on election day was the result of people voting tactically due to FPTP. As such, for the adjusted model, I’ve applied a proportionate adjustment to the first preference votes in each constituency, to make the national tallies add up to what the pre-election polls were predicting. It’s hoped that this adjusted model can better capture the true first preferences of voters than the simple one.

Anyway, on to the results. After running through the model for each set of assumptions, here are the predicted seat totals for the simple AV model (AV-Smp), the adjusted AV model (AV-Adj) and the actual election results for reference (FPTP):

What’s immediately obvious is that, as would be expected, the Lib Dems gain the most benefit from the new system, as they’re the party most disadvantaged by FPTP. What might be surprising, though, is quite how much they benefit from it when you look at the adjusted model. It’s often pointed out that AV is not a truly proportional electoral system, which is quite true. However, my model suggests that it would be far more proportional than the current system, with the Lib Dems winning 23% of the seats on 27% of the vote, rather than the current 9% of the seats on 24% of the vote.

The model also suggests that coalition government could well become the norm under AV, as under both simulations a government would need any two of the big three parties to form a majority. Nonetheless, this simulation is being applied to an outlier election in the first place, and it’s still entirely possible for parties to gain an overall majority under alternative vote.

It’s worth pointing out that this isn’t developed as a predictive model of elections under AV; it’s a simulation of what might have been on May 6th, not what will happen in future elections. I might amend it in future to analyze likely results in the next election (if it’s held under AV), but the output will be unlikely to closely reflect what you see above, due to changes in political dynamics between elections. The Lib Dems, for example, are likely to lose out on transfers from Labour and independents after going into government with the Tories, but will be more transfer-friendly to Tory voters.

Methodology

The results for each constituency were taken from the Press Association’s website, taking the corrected results where appropriate. In taking down candidates’ parties, I modeled the following parties:

• Conservative
• Labour
• Liberal Democrat
• DUP
• SNP
• Sinn Fein
• Plaid Cymru
• SDLP
• Green Party
• Alliance
• UKIP
• BNP
• UCUNF
• TUV

All other candidates were counted as independents, as modeling any of the smaller parties would have been very difficult and unlikely to have any impact on the final result anyway.

After taking down the results of each party in each constituency, I split the constituencies between those from England, Scotland, Wales and Northern Ireland. This was necessary due to the effect of the regional parties, and the variances in likely transfer rates between different parties in different regions. I had considered splitting England into different regions for modeling purposes, but decided against it as I didn’t feel that I had enough polling data to confidently estimate the difference in transfer patterns between the regions. Nonetheless, separating Scotland and Wales (and, of course, Northern Ireland) was still necessary due to the regional parties, and clearer transfer differences.

Transfer Tables

To model the transfer rates between each of the parties, I primarily used the data from a ComRes poll from the 26th of April, where they asked a question on what party respondents would give a hypothetical second preference to. This poll would be quite reliable for proportional transfer rates between the three main parties, but barely reliable at all for transfer rates to and from the smaller parties, due to the small sample size for each. As such, for the numbers below, the transfer ratios between the main parties closely resemble the proportions from the poll, but the numbers for the smaller parties were mainly educated estimates, with the invaluable assistance of Ed Gaffney in formulating them. It’s worth noting that the model wouldn’t be particularly sensitive to transfer rates for the smaller parties, so even if these numbers are off, it won’t have a huge effect on the results.

Consideration also has to be give to the fact that the poll in question suggests a much bigger number of first-preference Liberal Democrat voters than was actually the case (and a similarly smaller number of Tory and Labour voters). Second preferences aren’t going to be independent from first preferences, so it’s likely that a poll which showed accurate first preferences would have given slightly different second preference distributions. Unfortunately there weren’t any polls at all close to the election that got the result correct, and as far as I can tell none of the older polls asked the second preference question. As such, I’ve decided to stick to the ComRes poll in question, as it’s the most reliable I can find, and would quite well fit the adjusted model in any case.

The transfer ratios between each party in each of the four regions I’ve modeled are as follows, and are the same for each version of the model:

The tables are to be read along each row, with the eliminated party in the first column. For example, if a Labour candidate is eliminated in an English constituency, 10% of his votes will be transferred to the Tory candidate, 67% of them to the Lib Dem candidate, 5% to the Green candidate, etc. ‘N/T’ is the proportion of non-transferrable votes, ie. ballots where the voter didn’t fill in a second preference.

Operation

The model goes through each constituency and simply simulates each round of transfers under AV. So, the candidate with the fewest votes gets eliminated first, and his votes are transferred to each of the other candidates according to the appropriate entries in the tables above. Then, the remaining candidate with the fewest votes is eliminated, and his votes are transferred, and so on. Before each round of transfers, if any candidate already has over 50% of the vote, he’s declared the winner, and the model takes down the winning party and moves on to the next constituency.

Between each round of transfers, the model ‘normalizes’ the transfer matrix that it uses to calculate how many votes transfer to each party. It does this by zeroing the entries for transfers to any parties which are no longer in the running, and then proportionally increasing the transfer rates to each of the other parties to make sure they sum to 100%. In this way, the model appropriately handles the elimination of parties between different rounds of voting and ensures all votes are properly accounted for, without any transfers to ‘ghost candidates’ who have already been eliminated.

As an example of how this works, if there are only three candidates left after a few rounds of transfers in an English constituency; one Tory, one Labour and one Lib Dem, and the Tory is to be eliminated, his votes will be transferred at a rate of 12.2% to the Labour candidate, 67.1% to the Lib Dem, and 20.7% non-transferrable. You can see that these transfers are still in the same proportion to each other as they are in the table above, but have been increased to ensure 100% of the votes go to the remaining parties.

Between each round the model also recalculates the winning threshold based on 50% + 1 of the remaining votes, after having removed all the non-transferred votes from earlier rounds.

Adjusted Model

In estimating the first preference votes for my adjusted model, I took the simple average of the final polls from each pollster before the actual vote (taken from fivethirtyeight.com). These polls suggested that (excluding Northern Ireland), the Conservatives would have received 35.5% of the vote, Labour 27.4%, the Lib Dems 27.5% and others 9.6%. I then applied a proportional national swing, by multiplying each Conservative candidate’s vote by a factor of 0.96, each Labour candidate’s vote by 0.924, each Lib Dem candidate’s vote by 1.167 and all other candidates votes by 0.98. The national vote then added up to the numbers suggested by the polls.

I chose a proportional swing to model the vote shift, rather than a uniform national swing, or two main reasons. The first is technical; under a uniform national swing it’s possible for a candidate to end up with a negative number of votes, which not only makes no sense, but would completely mess up my model’s calculations. The second is simply that I feel a proportional swing is more appropriate to model a shift in a single election (particularly a three-way election), even if uniform national swing may have been more accurate in the past in modeling shifts between elections (and when there were only two viable parties).

Northern Ireland

In the Northern Ireland table, the entry ‘Ind Un’ is short for ‘Independent Unionist’ and is used for Sylvia Hermon and Rodney Connor, as I felt the standard ‘independent’ designation wouldn’t have been appropriate for them. Nonetheless, I would be very quick to admit that my model is far from appropriate for simulating the results in Northern Ireland. I included it in the model for completeness, but an accurate simulation of Northern Ireland would need a model that properly takes into account the unique political dynamic in the region, and designed by someone who understands that dynamic much better than I do. As it happened, my model actually didn’t predict any changes in NI constituencies.

Constituency-Level Modeling

Something I considered when designing the model was to make individual transfer tables for certain idiosyncratic constituencies, such as Brighton Pavilion, Buckingham and Wyre Forest. These constituencies have rather different dynamics due to particularly strong candidates from small parties, and as my model gives a relatively small proportion of transfers to independents and the smaller parties, it might not be entirely appropriate for them.

In the end, I made the deliberate decision to model these constituencies in exactly the same way I model all the others, rather than attempt to model them separately. There are a number of reasons I made this choice. Firstly, to appropriately model individual constituencies, I would need a level of local knowledge about each of these constituencies that I simply don’t have. Polling data isn’t available on individual constituencies, so any transfer ratios I could come up with would basically be complete guesses, and couldn’t be taken to be in any way reliable. Secondly, once I start modeling constituencies on an individual basis, I have to make choices as to which constituencies are worth separately modeling. Once again, this introduces an extra level of bias in terms of which constituencies I would choose to single out. I personally don’t have a good enough knowledge of constituency-level politics in the UK to make these decisions, neither do I have any objective way of determining which constituencies require special treatment.

My third reason for using a single model across all constituencies in any given region is simplicity. If my model is biased, I would prefer it to be a simple, consistent bias that can easily be taken into account by anyone interpreting the results. Once I start to model constituencies on an individual basis I’d be introducing a wide range of complex biases that would make it considerably more difficult to determine whether the overall results are valid or not.

That all being said, there are two constituencies that would be worth looking at for anyone interpreting the results. The first of those is Brighton Pavilion, where the Greens sensationally took a seat on the 6th of May. Both versions of my model give this seat to the Labour candidate after transfers. However, it’s entirely possible that the prominence of Caroline Lucas, the Green candidate in the constituency, would have helped her win enough transfers to take the seat.

The second constituency worth looking at is Wyre Forest. In this constituency, the outgoing MP was Richard Taylor, representing a local group known as ‘The Independent Community and Health Concern’, who was beaten by the Conservative candidate in the election. Both versions of my model give the seat to the Tories after transfers, but it’s actually probable that transfers from the Labour and Lib Dem candidates would have heavily favored Taylor, giving him the seat.

Software Used

The model was developed via a combination of Microsoft Excel and Applescript. I would have developed it entirely in Excel, using Visual Basic for the scripting, so that I could distribute it for others to use, but unfortunately Microsoft removed Basic support from the most recent version of Excel for Macs, so Applescript had to do the job instead. Nonetheless, while this combination may not have been particularly computationally efficient, it helped me keep an eye on everything to make sure the model was running as expected.

These past few days have seen the downfall of Enda Kenny as leader of Fine Gael. Following the sacking of Richard Bruton, his leadership became untenable, following the resignations of nine further members of his front bench, his leadership became impossible. What is most unfortunate about the whole affair is that, after four decades of political life, Kenny’s career should come to an end with him trying so desperately to cling to power, damaging both himself and the party in the process.

Yesterday afternoon he had an opportunity to change that. After witnessing the resignations of most of his front bench, he was due to speak for a vote of no confidence in the Taoiseach, a situation where he, not Brian Cowen, would paradoxically be at the center of the Dáil’s attention. I had hoped that he may have taken that opportunity to make a speech that would be worth capping a political career with, but unfortunately he gave the same speech in the same way he always does, a speech that reminded many why they no longer wished for him to be their leader.

The following is, in a brief form, my humble opinion of what he should have said, of the kind of speech he should have given.

“This is not a time for business as usual, and it is not a time for politics as usual. If we are to recover as a nation, if we are to leave our children the Ireland they deserve, then we cannot keep along the same political path that is so well trodden in this country. We need a class of politicians for whom the notion of putting the interests of the country above their own is not simply rhetoric. We need a class of politicians who can pass that most difficult test of leadership, stepping aside.

This morning you and I were in very similar situations, Taoiseach. We are both leaders, and we both serve those who elect us. Over these past 24 hours I have come to accept that those who elect me, the Fine Gael parliamentary party, no longer have confidence in me, and that the only honorable thing to do is to step down as leader of the party. It has been the most difficult decision of my life as a public servant, but one which has become inescapable to me if I wish to truly place the interests of my political party and the Irish public ahead of my own.

Over the course of weeks, months, and indeed years, you too must have come to the realization that the people of this nation, the people you serve, no longer have confidence in you as their leader. Beneath all the bravado, beneath all the rhetoric, deep within you you have come to the same inescapable conclusion that I have over these past few days. It is not an easy realization to come to, Taoiseach, it is that one fear that shakes a politician to his very core, and it is that one truth that is hardest for us to accept.

Tomorrow I will be stepping aside, accepting my fate and doing what is best for the country. I ask you to do the same, to resign as Taoiseach, call a general election and allow the Irish people their right to choose a new government that truly represents them. It would not be an easy decision, it would require a courage, an honesty and a decency that have been lacking in politics for far too long. It would be a selfless decision that is worthy of a true statesman, a true democrat, and a true public servant. It would be a decision that could help signal a return to those highest of standards in political life that we so often talk about but so rarely act upon. Most importantly, it is a decision which you know in your heart to be right.

Put simply, Brian, it’s time for us to go.”

The Tories have been a minority party in UK politics for three-quarters of a century. That may seem odd, given that they’ve come out with an overall majority of MPs in nine elections since, but you have to go all the way back to Stanley Baldwin in 1931 to find the last leader of the Conservatives to lead the party to get over 50% of the votes in a general election*. Even in Margaret Thatcher’s 1983 landslide, the Tories only managed 44% of the vote, but won a large majority of seats as the opposition vote was split between Labour and the SDP/Liberal Alliance. Winston Churchill, now considered one of the greatest Prime Ministers of all time, never even actually won an election on the popular vote. During his three elections as Tory leader, he managed to win a majority of MPs in just one, and even then with a slightly lower percentage of the national vote than Labour.

The Conservatives know all this, and David Cameron, a former student of politics, knows it as well as an of them. The history of the Conservative party since universal suffrage has been of a declining popular vote, mitigated only by the gradual split of the center-left between Labour and the Liberals. With the UK’s first-past-the-post electoral system, this had been good enough to secure frequent parliamentary majorities for the Tories, but under any even remotely proportional system their hopes for an overall majority would almost completely disappear. Their choices would either be eternal opposition, or a shift to the left for occasional coalition governments. Neither are particularly appealing to die-hard Tories.

Even if they do promise electoral reform, simple game theory shows that they would never deliver on that promise. If any move towards proportionality was actually passed, the Lib Dems would have an immediate incentive to vote down the government, precipitate a general election under the new system and reap the spoils of a big increase of seats, with the Tories losing out. Conversely, if the Tories continually delay or water-down electoral reform proposals, the only power the Lib Dems have over them is to trigger an election under FPTP, in which the Tories would have a very good chance of getting an overall majority. The choice for the Tories would be between a probable increase in seats under a FPTP election, or a definite, permanent decrease in seats under a proportional election. It would be naive to the point of stupidity to believe that they’d ever choose the latter, no matter what promises they may make in coalition negotiations.

Hypothesis 2: The benefits of electoral reform to the Liberal Democrats far outweigh any concessions the Tories may give in a coalition government.

The Lib Dems were the big story of the election campaign. After Clegg’s performance in the TV debates, they managed to leapfrog Labour into what looked like a secure second-place in a polls and, even with the electoral system stacked against them, pretty much every observer assumed they’d make big gains in terms of seats. On the day, these gains completely failed to materialise, as even though their vote went up slightly, they still managed to lose 5 seats. What happened? Well, in simple terms, soft Labour supporters deserted them for fear that they’d prop up a Tory government, and soft Tory supporters deserted them for fear they’d prop up a Labour government. Coupled with a vote distribution where they made big gains in seats where they didn’t have a chance, and losses in a lot of their marginal seats, it added up to a pretty disastrous result for the party.

However the party may have underperformed, though, they ended up in the immensely powerful position where it’s effectively impossible to form a majority government without them. This is probably the only chance they’re going to get for at least a generation to have a real impact in national politics, and they need to use it wisely. They effectively have two choices; form a coalition with the Conservatives and try to push through Lib Dem policies within government (with or without places at the Cabinet table), or shack up with Labour and focus on electoral reform.

As explained above, any coalition with the Tories can’t credibly include electoral reform, so the Lib Dems would have to focus on getting seats at Cabinet and/or notable policy victories. On the Cabinet, their best possible outcome is having Vince Cable appointed Chancellor, which would give them quite a bit of power, but taint the party’s national image as they’ll be associated with the big spending cuts and tax rises that the Chancellor will inevitably have to make. Without a seat at cabinet, they can gain certain promises of policy implementation, but backbench Tories will be unlikely to allow them too much influence outside of the areas where the Lib Dems and Tories already agree. Both scenarios have a similar issue with the credibility of Tory promises; the Tories’ best strategy is to wait a few months to a year and call another general election, with a good chance of winning an overall majority. They can simply keep delaying the Lib Dems’ policies until that point.

After a year or so in government with the Tories, the Lib Dems would be thrust back out into the political wilderness. A chunk of left-wing vote would immediately desert them following the coalition with the Tories, and with memories of the 2010 election, voters would be suspicious for a generation or more of the party’s ability to make any real gains in seats, no matter what the polls say. Whatever they may be able to achieve in government, it’s unlikely to be worth decades of political irrelevance.

Which leaves Labour.

Hypothesis 3: Labour are willing, and capable of implementing electoral reform with the Liberal Democrats.

Unlike the Tories, Labour have been making big signals in favour of electoral reform, both before, and especially since, the election. While they’ve failed to do so since coming to power in 1997, there’s good reason to believe they’re actually serious this time around. For one, while they would also be hugely unlikely to form a majority government themselves under a proportional system, they’re in general much happier with the idea of coalition government than the Tories are, as they consider the Lib Dems to be a fairly good fit in terms of a partner for a center-left government. The fact that the Tories would never have the chance to form a government alone again would certainly make reform that much more appealing to Labour back-benchers.

More importantly, a promise by Labour toward electoral reform would be completely credible from a Lib Dems point of view. Consider the number of seats such a coalition would have. Labour, plus the SDLP and Sylvia Hermon, who vote with them, have 262 seats, and the Lib Dems and Alliance have 58. With Sinn Fein abstentionism, they’ll need 323 seats for a majority, which means they’re two short, and will have to get either the SNP or Plaid Cymru on board for a tiny majority. Everyone involved would know that the government would be inherently unstable, and it’s precisely this instability which would give credibility to a Labour promise to electoral reform; the government couldn’t possibly hold itself together long enough to do anything else.

Labour and the Lib Dems could come to a simple agreement; form a new parliament, and almost immediately pass a single bill, calling a referendum on electoral reform. The coalition would only need to hold itself together for a single vote, which could be won with the support of the SNP and Plaid Cymru, and likely the Greens’ new MP, all of whom stand to gain from a more proportional system. The only plausible reform that could be implemented would be Instant Run-off Voting, which was proposed by Gordon Brown before the election under the name ‘Alternative Vote’. Not only would it be supported by all parties involved, but by leaving the constituencies as they are it could be implemented much more quickly than any system that requires the creation of multi-seat constituencies.

IRV also has the benefit of being far more likely to pass in a referendum. It keeps the single-seat constituencies exactly as they are, and in the majority of cases, people’s MPs would be the same as elected under the old system. It also has the perhaps unexpected side-effect that the BNP and other extremist parties would actually be less likely to get a seat under it than under FPTP, assuaging common fears that proportional representation would open the gateways to a swathe of BNP MPs. The effects of the reform would probably be a sizable increase in Lib Dem seats, a small decrease in Labour seats and quite a large decrease in Tory seats, with perhaps a couple of extra seats for the regional parties.

With indications that Brown may be willing to step down as Labour leader as part of a deal, this scenario would also present the perfect opportunity to have a somewhat orderly leadership election in the party, which could happen during the weeks leading up to the referendum. A new Labour leader, elected maybe a few days after the referendum result, could then immediately ask the Queen to dissolve Parliament, precipitating a new election under the new rules. This new leader could then credibly lead a coalition government with the Lib Dems after the election, having removed the taint of Brown and receiving his/her own mandate.

Trying to form such a short term arrangement with Labour would undoubtedly be messy for the Lib Dems. It would leave Gordon Brown as PM, even if only for a few weeks. It would require the parties to run a referendum campaign (something they’re not used to in the UK), while at the same time preparing for a second general election in as many months. It may well irritate voters who don’t want to have to go to the polls two more times before they see a stable government. It will seem opportunist for the Lib Dems to push for an electoral reform referendum when the country is in a fiscal hole and needs a stable government. It will also be difficult for Clegg to rebuff the Tories after Cameron has (in public, at least) been portraying himself as very open to Lib Dem involvement in a Conservative-led government.

But, for all this, it’s still the Liberal Democrats’ best choice. This is their only chance in a generation to implement the sort of reform that they need to become a significant force in British politics. It would be easier, more expedient and politically safer in the short term to take Cameron’s offer and side with the Tories, but it would be a mistake, one which may well prevent the Liberal Democrats from ever getting the chance to serve in government again.

* Not only was this election the only time under universal suffrage that any party actually got a majority of the votes, but it would interest those Tories with an instinctive fear of coalition to know that, even though they had a huge majority of seats, the Tories still went into coalition following the election, serving under Ramsay MacDonald, former Labour PM, as Prime Minister.

There are a few different systems used or proposed to combat this. The first, and probably the simplest, is to just randomize the positioning of candidates on the ballot paper. From one election to the next, this does prevent a candidate like Aaronson appearing on top of the ballot every time. However, in any given election there is still one candidate who appears on the top of every ballot, and hence receives an advantage from that position. Likewise, one candidate will be unfortunate enough to be on the bottom of every ballot, and will be similarly disadvantaged.

A more sophisticated approach uses multiple ballots for each election. A good example of such a system is the one used for elections in Tasmania, which is known as Robson rotation. It comes up quite often in discussion of ballot paper ordering and was recently proposed for use in Ireland by Barry Cahill, in a submission to the Joint Oireachtas Committee on the Constitution. With Robson rotation, the election officials print a number of different ballots equal to the number of candidates, with the positions of candidates on each ballot ‘rotated’ between ballots*. Voters are then randomly given one of the different ballots.

As an example, consider an election with six candidates; Mr Aaronson, Ms Babich, Mr Clayton, Mr Dexter, Mr Egan and Ms Farrell. Under a simple rotation system, there would then be six different ballots printed with the ordering of the candidates as follows:

Example 1:

When a voter comes in to the polling station, she’ll be randomly given one of those six ballot papers. The appeal of this system should be fairly clear. Each candidate appears on the top of exactly 1/6th of ballots, in the second position on exactly 1/6th of ballots, etc. Hence, no candidate should be advantaged or disadvantaged by their positioning on the ballots, and the vote should be truly unbiased.

Unfortunately, this approach fails to take into account one important aspect of voting: political parties**. In the PR-STV elections we hold in Ireland, parties often run multiple candidates in a given constituency, with the hope of picking up more than one seat. Furthermore, it is quite common for a voter to go into a ballot booth with the intention of voting for a particular party, but not caring too much about which of that party’s candidates gets elected.

To extend the example above, let’s now consider than there are four political parties, the Blue Party, the Red Party, the Yellow Party and the Green Party. Aaronson and Babich belong to the Blue Party, Clayton and Egan to the Red Party, Dexter to the Yellow Party and Farrell to the Green Party. Now, imagine a voter who wants to vote for the Blue Party, but doesn’t really care about Aaronson or Babich, and will just give a number 1 vote to the Blue candidate who comes first on the ballot, and a number 2 vote to the Blue candidate who comes second. Here’s how this voter would fill in each of the ballots above:

Example 2:

Here you’ll see a problem; for a voter who votes along purely party lines, ignoring the candidates, Mr Aaronson will get the first preference in five out of the six ballots, whereas only one ballot favours Ms Babich. A similar bias would occur amongst voters for the Red Party, where Mr Clayton is placed above Mr Egan on four of the six ballots. The challenge, then, is to produce a set of ballots where such an intra-party bias wouldn’t exist.

In that case, consider a new ballot ordering system. First, take the odd-numbered ballots produced by simple rotation. In our example, these would be ballots 1, 3 and 5. Then, produce a reversed version of each of these ballots as well. For our candidates, the ballots would then be as follows:

Example 3:

If you look closely, you’ll notice that this system is pairwise unbiased. That is, for any two candidates, each of them appear ahead of the other on exactly half the ballots. What’s more, it’s also positionally unbiased, in that each candidate appears in each position on an equal number of ballots. It even manages to do so with the same number of ballots as simple rotation, which is positionally unbiased, but not pairwise unbiased.

Unfortunately, while this system works quite neatly where there are an even number of candidates such as in the example, a slightly different scheme is needed when there number of candidates is odd. The reason for this is that, for an ordering system to be pairwise unbiased, it has to have an even number of ballot papers. Furthermore, for it to be positionally unbiased, it has to have a number of ballot papers that is a multiple of the number of candidates. Together, these mean that the optimal number of ballot papers for an election with an odd number of candidates is exactly twice the number of candidates. The simplest way of fulfilling both criteria is to produce a set of ballots using the simple rotation method, and then to also use a reversed version of each of those ballots. Where there are 5 candidates, for simplicity A, B, C, D and E, we’d get the following ballots:

Example 4:

Although this system for an odd number of candidates requires more ballot papers, it successfully satisfies being both positionally and pairwise unbiased. If the two systems illustrated in examples 3 and 4 were to be implemented in a set of elections, with the first used in constituencies with an even number of candidates, and the second used in constituencies with an odd number, then the total number of ballots to be produced would average only 50% more than under simple rotation, but with the considerable advantage of being unbiased between any given pair of candidates.

You can actually take the criterion of being pairwise unbiased another step further, though. Let’s consider, for example, that a party is running three candidates in an election, with the same kind of party-linear voter as found in example 2. In this case, we might want the ballots to be 3-wise unbiased. With three candidates, there are 6 different possible permutations of those candidates. Hence, for a set of ballots to be 3-wise unbiased, the relative positions of any group of three candidates must appear in each of the possible permutations on exactly 1/6th of the ballots. In order to achieve this, the number of ballots must be a multiple of six.

If this sounds complicated, it’s because it is. Even in the case of there being six candidates, where it should be possible to do so with just six ballots, I’ve been unable to devise a set of ballots which is 3-wise unbiased. It gets more difficult as the number of candidates increases (and also, for those mathematically inclined, if the number of candidates is coprime to 6), with a 13-candidate election requiring a minimum of 78 ballots to be both positionally unbiased and 3-wise unbiased. Fortunately, any set of ballots which is 3-wise unbiased is also pairwise unbiased, so it’s not a matter of choosing between the two.

The concepts of being pairwise unbiased and 3-wise unbiased can of course be generalised to a set of ballots being n-wise unbiased for any number n. Choosing higher degrees of this criterion can make things very difficult for election officials, though; if you want to make an 11 candidate election positionally unbiased and 5-wise unbiased, you’ll need at least 1320 different ballots to be printed. The furthest you can push this is to use the total number of candidates as the n in n-wise unbiased. In this case, you’re simply printing every possible permutation of candidates, and you’ll quickly end up with more ballot variations than there are voters to give the ballots to.

In the end, the designing of ballot papers, and what degree of bias to protect against, is a matter of how much complexity election officials are prepared to deal with. Currently, we list candidates in an alphabetical order, which is the simplest method, but also by far the most biased. A good target would be to produce a set of ballots that is both positionally unbiased and pairwise unbiased, which would require a number of ballots one and a half times the number of candidates, but be considerably less unbiased that the status quo, even combatting the effects of party-linear voters. A 3-wise unbiased system may be worthwhile, depending on the number of candidates expected to contend an election, but going any further than that would increase the complexity of the system massively while only making negligible reductions of the effective bias of the ballots.

* Robson rotation, as originally designed, is actually somewhat more complicated than the simple rotation system I describe here, as it uses an element of randomness in the rotation system.

** In elections to the Tasmanian House of Assembly, this is actually accounted for by listing candidates from each party separately, rather than a single long list, and then using Robson rotation within each party’s candidates. A similar system is used in the Australian Capital Territory. These systems require considerably more ballot papers to be printed, though; an election in the ACT where a party has 7 candidates requires the printing of 420 different ballot papers. This isn’t used for elections to the Tasmanian Legislative Council or in Tasmanian local elections, though, where candidates of all parties are placed on a single list.

1. Willie O’Dea’s resignation from the cabinet
   With O’Dea gone from the Department of Defense, a cabinet reshuffle is now inevitable. While many are speculating that Cowen will simply appoint one of the junior ministers to fill O’Dea’s post, he hasn’t reshuffled his cabinet since taking office in 2008 (in a very different economic climate), and now would be the perfect time to do so. What’s more, with a vacant seat on the cabinet, an independent minister could be brought in without having to relegate any of the sitting Fianna Fail ministers to the backbenches. This could help diffuse any animosity that the FF parliamentary party might have about bringing in someone from outside Fianna Fail.
2. Deirdre de Burca’s resignation from the Seanad
   As well as an opening in the cabinet, there’s now an opening in the Seanad, thanks to Deirdre de Burca. As she occupied one of the 11 Seanad seats reserved for nominees of the Taoiseach, Brian Cowen can now appoint whoever he likes, at as short notice as he likes, to replace her. Indeed, he could nominate someone on Monday morning, and by Monday evening they could be sitting at the cabinet table. Of course, as the seat was previously held by a Green, the Green Party will undoubtedly want another of their own to replace her. Cowen would do well to remind them that Fianna Fail recently elected Niall O’Brolchain as an additional Green senator to replace Labour’s Alan Kelly, and that Cowen’s appointee would be independent, rather than from Fianna Fail. Of course, if that didn’t work, a promise of an additional junior minister post for the Greens in the reshuffle would probably do the trick.
3. Mary Coughlan’s cock-up over the Ryanair hangar proposal
   Mary Coughlan has made quite a few mistakes and gaffes during her tenure as Minister for Enterprise, Trade and Employment, but, at a time when unemployment is at its highest in a generation, her inability to secure 500 jobs that seemed to be offered on a plate by Ryanair is the first one to really make her position look untenable. What’s more, after O’Dea’s resignation, any further revelation in the Coughlan-Ryanair saga could have catastrophic consequences for the government. It would be best for Cowen to reassign her to a different portfolio as part of a wider cabinet reshuffle, which would prevent any arguments over her handling of Ryanair’s proposals from becoming a resigning matter. In order to illustrate that her movement out of the portfolio is simply part of the reshuffle and not a demotion, she could keep the position of Tanaiste in her new role.
4. Greece’s future is still shaky
   Within the the next week, Greece is expected to try to raise up to €5 billion euros from international bond markets, which will be a big test of market confidence in their finances. If Greece struggles through this test, renewed pressure will come not only on them, but also on the other ‘peripheral countries’ in the eurozone, including Ireland. Brian Lenihan’s budget in December bought us a bit of leeway compared to Greece, Spain and Portugal, but we can’t count on that goodwill from the markets to last forever, and now would be a very good time to differentiate ourselves once again, by bringing in an outside expert to a major economic post on the cabinet. By picking the right person, and handling the international press well, any potential fallout from Greece’s problems could be neatly defected, keeping our own borrowing within reasonable costs.

I had previously suggested Jim O’Hara to take over the role of Minister for Enterprise, Trade and Employment, and I still think that he would be a very good choice. Of course, so long as Cowen were to avoid appointing anyone who was in any way involved in either the property or finance industries, there are quite a few successful Irish businessmen and businesswomen who would fit the bill, including some of the members of the Taoiseach’s own innovation taskforce. The important thing is to appoint someone who would be respected by the international business community, with any experience in high-tech exports as an added bonus.

Whoever Cowen were to choose, he now has a perfect opportunity to create a rare piece of good news for the government, and to end a dreadful couple of weeks for his party (and Irish politics as a whole) on a high note. Of course, whether he has the fortitude to make good on this opportunity is a different matter entirely…

Which leads me to my question for those with more knowledge of financial regulation than I do; why not make capital requirements non-linear with regard to the size of the bank? Or, in more simple terms, why not force bigger banks to keep a higher percentage of their deposits in safe assets than smaller banks do? The reasoning for this is fairly straightforward; small banks can have a relatively high failure rate without posing systemic risk to the wider financial sector, whereas the fall of a single large bank can be catastrophic for the entire economy (hence the phrase ‘too big to fail’). The structure of capital requirements could be rejigged such that small banks would have modest capital requirements, and as bank size increases, so do their capital requirements. This could be continued to the extent that once a bank became ‘too big to fail’, its capital requirements would be almost 100% (making it in effect a narrow bank), meaning it would become, in theory at least, ‘too stable to fail’.

Unlike an across-the-board increase in capital requirements, such a system of non-linear capital requirements would give smaller institutions the capacity to continue with a healthy level of lending, while still ensuring that the largest banks are sufficiently stable. Furthermore, it would have the advantage of not requiring an explicit cap on the size of banks (which in fact already exists in the US, but has been repeatedly breached over the past couple of decades). Instead, the market itself would settle the appropriate sizes for banks, balancing between the needs of stability and lending capacity.

Fast forward to 2010, though, and the climate change bill that’s moving from Congress to the Senate is far removed from Obama’s system, with a whopping 85% of credits being allocated by Congress and only 15% to be auctioned. This doesn’t just defeat the purpose of a cap-and-trade system, but is actually worse than no bill at all. By giving congressmen the power to allocate hundreds of billions of dollars worth of credits, the bill would create a volume of pork that even the most cynical of Washington-watchers would never have thought possible. The system would be a goldmine for lobbyists, and the credits would end up mainly in the hands of the most highly polluting industries, leaving lower-polluting companies to buy them via auction, and ironically shouldering the higher costs.

There are two main reasons given for the free allocation of credits rather than auctioning. The first is that auctioning credits would cause energy prices to go up, causing extra expense for ordinary families. The logic is that, by giving energy companies free credits, they won’t increase their prices. The first problem with this is that the logic is wrong, energy companies will increase prices whether they pay for emissions credits or get them for free. The second problem is that, for a cap-and-trade system to work, energy prices have to go up, to get people to reduce their usage. If you want to counteract the extra hardship that these higher prices will cause to lower and middle income families, then do so through tax breaks or extra lump-sum payments, don’t just attempt (futilely) to keep prices low.

The second argument is that, by increasing costs for high-emissions industries, people who work in these industries will end up losing their jobs. This is true, but the approach of simply giving these industries billions of dollars worth of free credits is massively counter-productive, and completely defeats the purpose of the cap-and-trade system. Any attempt to help those people (and often entire communities) who would lose out from a cap-and-trade system should be focussed on helping the people themselves, not just bailing out the companies they work for.

The problem is that an auction-only system couldn’t credibly get through both Congress and the Senate without some big pressure from the White House. All it takes is for a single congressman or senator to propose an amendment to allocate a tiny minority of credits for free to a favoured company in order to ’save jobs’, and the floodgates open for everyone else to do the same for whatever pressure groups they have to deal with back in their home state. The promise of all that pork is what’s twisted the President’s original proposals into one where 85% of credits are auctioned. If Obama wants a climate change bill that actually works, he’ll have to make it very clear to congress that he’ll veto any bill without a fully functional cap-and-trade system where 100% of the credits are auctioned off.

Of course, this would be a hugely risky move for Obama to make. Even in its current pork-filled form, the cap-and-trade bill is having huge difficulties finding its way into law. Hence, in order to give an auction-only bill any chance of passing both houses, some fairly large carrots will be needed to get enough congressmen and senators from both parties onboard. What Obama has to keep in mind is that, by fully auctioning the credits, the money brought in will give him the opportunity for some big, and potentially very popular additions to the bill. For example, he could…

Half the federal corporate tax rates

Despite priding itself as a pro-business economy, corporate tax in the US is actually amongst the highest in the developed world, with marginal rates as high as 38% and an average effective rate of 25.2%. While successive administrations (particularly Republican ones) would have loved to reduce the tax rates to make the economy more competitive, it brings in a lot of money to the federal government (estimated at $222 billion in 2010), so reducing rates would have entailed either making big increases to other taxes, or big reductions in spending, neither of which would be particularly palatable. Obama has a big opportunity here, though. Estimates put the revenue from a fully auctioned cap-and-trade system at between $130 and $370 billion a year in the short term. Even at the lower end of this scale, he could afford to half corporate tax and still bring in $20 billion in extra revenue.

This would be hugely welcomed by the business community. For companies in the low and middle-emissions brackets, the reduction in corporate tax would far outweigh the costs of the cap-and-trade system, which would create a big, powerful lobby in favour of Obama’s auction-only bill. It could also bring a lot of Republicans on board, who would be willing to stomach the credit auctions to support the reduction in corporate tax rates.

Create a $100 billion fund to help those who lose their jobs

In the transition to a low-carbon economy, it’s an unfortunate inevitability that employment shifts from high-emitting to low-emitting industries, resulting in a difficult few years for those who lose their jobs as part of this shift. While it’s not possible to prevent job losses in any functioning scheme to reduce emissions, it is possible to make the transition as easy as possible for those who are affected by it, and Obama could promise a fund of $100 billion to help them find new, stable employment in lower-emitting sectors.

The fund could operate in a number of ways. Firstly, a lump sum could be paid out to anyone who loses their job in a high-emissions industry, to help them cover a (hopefully short) period of unemployment. The government could then also pay for retraining and education to increase employability in new industries. To help their prospects further, generous tax breaks could be given to any low/medium emitting company who hires these workers.

A further issue is that there are many towns and cities where the main source of employment is in high-emissions industry, meaning there simply aren’t enough lower-emitting businesses to take on the number of workers who lose their jobs. In this case the fund could be used to give extra tax breaks to low-emissions companies that set up in these areas, creating new sources of employment.

With a $100 billion fund spread over the first 5 years or so of the cap-and-trade system, the payments and tax breaks could be very generous and make a significant difference to the people and communities affected by this shift to low-emissions industry. Furthermore, the cost of the fund would be more than covered by the revenues from the credit auctions, even taking into account the reduction in corporate taxes, so wouldn’t increase the deficit even over the short term.

Reduce taxes for low and middle-earners to counter the increase in energy costs

Another inevitability, as explained above, of the cap-and-trade system is that energy prices go up. This is actually desirable, as it encourages people to reduce usage (or switch to lower-emission energy sources), but it can cause difficulties for those on lower incomes who spend a disproportionate level of their earnings on energy usage. The solution to this isn’t in quixotic attempts to keep prices down, but simply to reduce taxes for low and middle-earners in proportion to the increased costs. Doing so would cost in the region of $50 billion a year in lost tax revenue, but in most scenarios this would be recouped by revenue from the credit auctions.

Set long-term emissions reduction levels, and back them up with carbon bonds

With the economy still struggling, Congress (and the US public) are unlikely to be willing to stomach big cuts in emissions levels in the short term. As a result, any cap-and-trade bill capable of passing will have to stick to fairly modest reductions in emissions over the first decade or so, with the bigger reductions kicking in after that point (the Waxman bill from 2007 proposed an allocation schedule that would work quite well). To foster business confidence and prevent future administrations from simply changing the allowances at a whim, the government would have to begin issuing carbon bonds based on these proposed caps, with 10 and 20 year maturities (perhaps extending to 30 year bonds if there’s a market for them). This would greatly increase investment in low-emissions industry and technology, as companies could insure themselves against future changes to the cap-and-trade system.

By combining a fully-auctioned cap-and-trade system with the above proposals, Obama could counter the big assumption that almost all doubters have about any emissions reduction scheme; that it would inevitably harm businesses and the economy. By recycling the auction revenue into a dramatic reduction in corporate tax, the overall scheme would actually be a significant boost to the vast majority of businesses. Only the most highly polluting businesses would feel the brunt of the carbon credit costs, and instead of bailing out the polluters, a $100 billion fund would be set up to bail out the workers affected by this, and help them find new work in the growing low-emissions industries. Finally, by selling carbon bonds, the US would set itself up as by far the safest country in the world to make long-term investments in low-emissions businesses, leapfrogging countries where there is less certainty over long-term climate policy. In addition to all this, there would still be enough left from the auction revenues to reduce the budget deficit by as much as $100 billion a year.

Edit (30/03/2010): This post was originally written using the term ‘green bonds’. I’ve since changed all references to ‘carbon bonds’ instead. This is to bring the terminology closer to that used by Michael Mainelli and Jan-Peter Onstwedder in a proposal made last year, where they used the term ‘index-linked carbon bonds’ to describe effectively the same thing. The change should also remove any confusion with other uses of the term ‘green bonds’.

You might expect a government with such an attachment to the notion of Ireland being a high-tech hub to have some sort of record of positioning the country as an international leader in the field over the past decade. The reality as it turns out, is quite the opposite. It’s not just that we’re not at the top of the international league tables on this, we’re actually, in a word, shit.

The quality of broadband provision in a country is an important indicator of technological advancement, but most people are well aware of how poorly we rank in that regard (if not, see here), so I won’t deal with that today. Instead, I’m going to look at the World Economic Forum’s Global Information Technology Report, which is released annually and ranks 134 countries on a wide variety of IT-related measures. The headline statistic (and pretty much the only one that you’ll hear reported in the media) is the Networked Readiness Index, in which Ireland ranks 23rd. This doesn’t sound too bad (although certainly isn’t as high as a ’smart economy’ would want to be), but this overall statistic takes into account quite a number of criteria that are only indirectly related to IT, such as ‘judicial independence‘, ‘property rights‘, etc. Essentially, we get extra points for not being a tinpot dictatorship.

Fortunately, the WEF breaks the stats down on a country by country basis, so we can see exactly how the government’s record compares on the real IT issues. Some of these are frankly shocking. Take ‘Internet access in schools‘, for example, where we’re ranked a very poor 44th. We dropped 6 places on this ranking from 2008 to 2009, and we’re now behind Thailand, Lithuania and Malaysia. We can hardly say that we’re equipping our children to take part in a future smart economy if we can’t even provide schools with basic internet access.

If you’re wondering why our schools have such poor broadband, maybe the next ranking will give you an indication. In ‘Importance of ICT to government vision of the future‘, we rank 46th, which is a drop of an entire 12 places from 2008. Among the countries to overtake us in the past year are the Dominican Republic, Mauritius, and Kazakhstan. That’s not to mention Gambia and Burkina Faso, who were already ahead of us. The WEF calculate this ranking on the basis of a survey of business executives worldwide, and they don’t seem all that convinced that repeating the term smart economy over and over again constitutes a plan for the future.

Another category that’s based on a survey of executives (ie the people who decide whether Ireland is a smart economy worth investing in or not), is ‘Government prioritization of ICT‘. Unlike the previous category, this is based on what the government is doing now, not what they plan to do in the future, and the results are even worse. In 2009 we ranked 68th, a drop of no less than 16 places from the year before. To put that in perspective, Gambia ranks over 50 places above us, and there are another 8 african countries that manage to prioritize IT more than our government does.

The last category I’ll bring your attention to is ‘Government success in ICT promotion‘, where we rank 66th. This also represents a drop of 16 places from 2008, during which time we’ve been overtaken by such countries as Vietnam, Colombia, Uganda and Kenya. Think about that last one for a second. In the time between the 2008 edition of the report being compiled (late 2007) and the 2009 edition (late 2008), Kenya had to deal with the aftermath of a rigged presidential election, where widespread ethnic violence killed 800 people, displaced 600,000 and brought the country to the verge of civil war. And amongst all that, Kenya’s government still managed to be more successful in promoting IT than Ireland’s.

And that’s the reality of the situation. For all the talk and all the hype, a country that we’re over 70 times wealthier than and is a hair’s breadth away from civil war is still more successful in promoting a smart economy than we are. It kind of puts Brian Cowen’s platitudes in perspective, doesn’t it?

When Proportional Representation by Single Transferrable Vote (PR-STV) was first established as Ireland’s electoral system in 1921, it was presented as an alternative to the first-past-the-post  (FPTP) system employed in the UK. The main reason that the new system was adopted was that, as its name suggests, it is more proportional than FPTP, in that the number of seats each party wins should be roughly proportional to the share of the vote they receive. While PR-STV has certainly improved from FPTP in that regard (not a difficult feat, as FPTP is particularly disproportional), it is worth noting that Ireland was the first country to implement PR-STV in national elections, and hence there was little evidence at the time it was chosen with which to analyze its proportionality. With almost a century of elections now held under the system, however, there’s now a considerable amount of data with which to examine whether PR-STV fulfils its purpose of proportionality.

The above graph shows the correlation between the proportion of national first-preference votes (FPV) a party receives and the number of seats it wins as a result. It is based on the results of every party in every general election held since 1981 (the first 166-member Dáil), and each point on the graph represents a party’s result in one of those elections. The dashed red line represents a perfectly proportional allocation of seats according to national vote.

What’s immediately visible about our current PR-STV system from the graph is how it benefits the larger parties compared to a perfectly proportional system. In only one outlying case did either of the state’s two large parties win less seats than would have been allocated proportionally (FG, 2002), and in every other election they received a bonus from the PR-STV system. For Fianna Fail in the 1997 and 2002 elections, this bonus gave them an extra 12 and 13 TDs, respectively, over their representation in a purely proportional system.

The PR-STV system, as currently implemented, likewise disadvantages smaller parties.  The second graph is enlarged to only show the results of parties that received less than 8% of the national FPV. It can be seen that in the considerable majority of cases, parties in this bracket win less seats than a proportional system would allocate them. Furthermore, there are often large variations in the number of seats won on a similar proportion of the vote. For example, between the 1992 and 1997 elections, the Progressive Democrats went from 10 to 4 seats, despite receiving exactly the same proportion of the national vote on both occasions (4.7%). In a perfectly proportional system, they would have won 8 seats in each election.

In Ireland, tax on inheritances comes in the form of the Capital Acquisitions Tax (CAT). This tax, which also covers gifts, was increased from a nominal rate of 20% to 22% in the April budget, but due to a range of exemptions and reductions that cover pretty much anything anyone would ever be likely to inherit, the actual effective rate will top out at 2% even on the largest inheritances, and in the vast majority of cases will be zero.

The threshold for CAT (where the beneficiary is a child, which covers most cases) is just over €520,000, with the tax levied at a rate of 22% on values over that. On their own, this threshold and rate would result in a situation where no tax on inheritance is paid in the majority of cases, and only a very small amount is paid by anyone other than the very wealthy. However, there are three reductions and exemptions that are applied that affect this situation massively. Firstly, residential property is completely exempt from CAT, regardless of value. In addition, reliefs are applied to agricultural and business property, in each case reducing their value by 90% when calculating CAT. What’s more, this reduction is applied before the threshold, which means the actual rate of CAT on both is 0% on values up to €5,200,000, and 2.2% on values over this.

To see the effect of this, consider the following example. Two people each come to own a farm with a value of €10 million. The first has inherited the farm from his parents, which means, after applying the relief, he pays €105,334 in tax on it, which is just over 1% of the overall value. The second person wasn’t quite so lucky as to be born into such a wealthy family, and buys the farm with her own income, which she has saved over a number of years. While working to save up all this money, she was paying income tax which, at a top effective marginal rate of 54%, meant that for every €1 she earned that would go towards the farm, she could keep 46 cent of it. Hence, in order to save the €10 million to buy the farm, she would have to actually earn €21,739,130 and pay €11,739,130 in income tax. This is ignoring stamp duty, or any other tax that would be applied on the actual purchase of the farm.

In both of these cases the person involved ends up with a farm worth €10 million, the difference being whether this wealth has been inherited or earned. In a just society one might expect that the taxation system would favour those who work for what they have over those who are lucky enough to inherit it. Our taxation system not only does the opposite, but favours those who inherit wealth to an astonishing degree; in the above example the person who actually worked for the farm had to pay well over 100 times as much tax as the person who inherited it. This notion of fairness isn’t merely philosophical, either. By not taxing inheritances to any significant degree, the government needs higher rates of VAT and income tax to make up the shortfall. People who work for their wealth are quite literally paying extra to give the children of wealthy parents the luxury of an almost tax-free inheritance.

Fairness aside, the current scenario simply doesn’t make any economic sense either. Almost all of the ways in which a government can raise revenue have unwelcome side effects. Setting corporation tax too high discourages foreign direct investment. A high rate of VAT discourages spending, which hurts businesses. Excessive income tax discourages people from seeking out higher-paid jobs, and can discourage them from working altogether if social welfare is generous enough. Comparatively, no matter how high you set inheritance tax, there are virtually no unwelcome side effects. The only possible side effect that you could attribute to an inheritance tax would be that it could discourage dying, which, if it somehow managed to do so, would be a quite welcome one indeed!

For a government, any tax which can be raised without hurting the economy should be a holy grail, especially in times like these. Bringing in a reasonable level of inheritance tax would save the government from having to raise other taxes or cut spending, and could hence help bring the deficit in line with minimal effect on the economy. Quite how much revenue an increased inheritance tax would raise is a complex question, and I hope to write a new post soon with a series of detailed estimates on what the answer might be under different circumstances

In the meantime, consider this; the government raised €292 million last year from CAT on inheritances. This is despite the fact that the largest component of inheritances (residential property) was completely exempt, and the next two largest (farm and business property) were taxed to an almost negligible degree. Even modest reform of inheritance tax should allow the government to bring in many times that figure, and this is hardly a time in which any revenue-raising technique can be ignored.