Tuesday, 19 April 2011

The Alternative Vote #5: Do the math

There are certain properties that you might expect a voting system to have. For example, you might think that a good voting system should choose the candidate with the majority of votes, or make it easier for candidates with more votes to win. These ideas have been formalised using mathematics in voting theory and social choice theory, so that comparisons can be made between different voting systems. In this post, Alisdair Cairns explores how AV performs as a system for collecting votes in comparison to First-past-the-post. 

Voting Theory is, predictably, the study of voting systems. One specific endeavour of voting theorists is to come up with rules that 'good' systems should adhere to. There are a multitude of potential criteria that have been suggested, and all can be seen as important depending on what you want from your voting system. I will attempt to explain a few of them and show examples of when FPTP and AV don't conform. It is however sometimes quite complicated to prove when they DO follow these rules, so you'll just have to take my word in those places!

1) Majority - "If more than 50 percent of voters put x as their most preferred candidate, then x should be elected."

This is maybe the most basic property and it is probably obvious that both FPTP and AV satisfy it. Not all voting systems do though. In fact it is not always obvious that the majority winner is the most appropriate. Consider this example:

Let candidates a, b and c be candidates in a vote and let xy represent a ballot where x is first preference and y is second preference.

ballot round 1
ab 9
bc 7
cb 1

a wins with a clear majority but b is at least the second choice for every single voter in the electorate. It might be that b and c voters REALLY hate candidate a, in which case it might be better overall if b were to win. Points-based voting systems, like Borda Count, cope better with this sort of situation.

2) Monotonicity - "A winning candidate should not be harmed if they are placed higher on some ballots." (Monotonicity is actually a whole system of inter-related statements but this formulation is simple and gives a good idea of what it's all about.)

On first glance it might be a confusingly obvious rule that a fair voting system should follow. But in fact AV actually fails this condition, as shown in the following election: 

ballot round 1 round 2
ab 8 14
bc 7 7
ca 6

Here c is eliminated first and its votes pass to a who claims a majority. However if two b voters had been convinced to switch to a then the situation would have looked like this:

ab 10 10
bc 5
ca 6 11

a has gained two extra votes but does worse because of it. Indeed it is because of this problem that tactical voting could still be prevalent under AV. The two voters who switched actually would have done better by voting for a candidate they didn't want!

FPTP has no such problems with monotonicity. If you get more votes, you stand a better chance of winning.

3) Participation - "The inclusion of additional ballots that have x above y should not change the winner from x to y."

This is closely related to monotonicity and seems equally obvious, but again AV fails miserably. Here's an example:

ab 7 7
ba 6 11
cb        5

Here c is eliminated first and its votes go to b who wins in the second round of voting. However if a few more voters had turned out in favour of c (but preferring b to a) then the situation might have looked like this:

ab 8 14
ba        6
cb 7 7

Those extra voters would have been better off not voting at all! This could feasibly be used as an argument that AV actually encourages voter apathy. 

Again, FPTP passes participation. Here a would win both elections.

4) Condorcet Criteria - "If there is a condorcet winner, they should win overall. If there is a condorcet loser, they should not win."

A condorcet winner, if one exists, is a candidate who beats every other candidate in pairwise comparisons. That is to say in an election between a,b,c…etc. if a and x were the only candidates, a would beat x for all other candidates x. Equally a condorcet loser is a candidate who would lose to every other candidate in pairwise comparisons. 

Instinctively these seem like pretty reasonable criteria. If a is preferable to every other candidate, on an individual basis, then surely they are the best candidate? In fact FPTP and AV both fail this criterion.

ac 5 7
bc 4 4
ca 2

In this election under AV, c is eliminated in the first round and a wins in the second. Clearly a would also win under FPTP. But in fact c is the condorcet winner! If either a or b were not running, then their votes would have been cast for c and so c would have won 7 to 4 or 6 to 5 respectively. 

Of course one could easily be suspicious of a situation where a candidate that is under 20 percent of the electorate's first choice could be the winner. Indeed some have suggested that voting systems should NOT satisfy the condorcet winner criterion!

Condorcet loser on the other hand is slightly weaker and possibly more appealing. Indeed AV passes where FPTP still fails:

ab 4
bc 3
cb 3

Here a is the condorcet loser as it would lose by 6 to 4 in pairwise comparisons to both b and c

5) Convexity - "If the electorate is split into two distinct, non-overlapping subsets and the winner in both is the same, then that winner should be the overall winner." 

Also known as consistency. Again this seems logical. Lets say we are placed in a constituency where the population is half urban and half rural. If a candidate wins among both the city and country voters then they should win the whole constituency, right? Not under AV:

Set 1 (urban)
ab 6 6
ba 4 7
cb 3

Set 2 (rural)
ab 3
ba 4 7
cb 6 6

ab 9 17
ba 8
cb 9 9

Clearly b wins in both subsets but when the electorate is considered as a whole she is eliminated in the first round. In fact in single-winner, preferential (candidates are ranked in order of preference) voting systems it has been proved that convexity and majority are mutually exclusive. If we want our voting system to satisfy both then we have to go with a system where only one choice is placed on the ballot, FPTP being the prime example.

Of course the votes in constituencies are never separated in this way, so it would be difficult to tell how often a problem occurs de to failure of convexity, but it is troubling to know that it could.

6) Clone Independence - "The addition of a candidate identical to one already present in an election will not cause the winner of the election to change."

Under FPTP, two very similar candidates suffer because they split the vote for that political stance, leaving the other parties to profit. Because of this, voting systems that don't satisfy clone independence encourage tactical voting. Voters you feel want to vote for a' may be encouraged to vote for a just so that b doesn't win. Here's an example where x' represents a candidate similar to x:

aa' 4 7
a'a 3
b 6 6

Under FPTP b wins very easily however under AV a wins. One could argue that if a and a' are so similar, it wouldn't matter if one were to simply stand down. But subtle differences can be important and a position where voters feel like their vote could be 'wasted' should be avoided at all costs. 

There are cases to be made for placing more or less importance on each of these rules (and the many, many more I haven't gone into) so I leave you to draw your own conclusions. Hopefully I have at least shown that there is very little in it from a purely mathematical point of view. It is perhaps obvious why Nick Clegg once described AV as a "miserable little compromise". 

Friday, 15 April 2011

The Alternative Vote #4: likely to lead to better or worse governments being elected?

 Charles Roddie is a Postdoctoral Fellow in Economics at Nuffield College, Oxford. In this essay he provides the most honest account I have read of why one might vote NO to AV: to avoid hung parliaments and left wing policies.

Is the Alternative Vote system a good idea?

What makes a voting system a good one?
AV is a proposed voting system for UK national elections, an alternative to the current first past the post (FPTP) system. The history is that Liberal Democrats have had a smaller share of representatives (MPs) than their vote share, and they would do better under other systems than first past the post, which favours the main two parties. Understandably, they feel very strongly about this, so when at the last election they were in the position of kingmaker, a referendum on AV was the main concession they required from the Conservatives to form a coalition government with them.

Now we are naturally getting a lot of arguments from the main parties rationalizing why they support or reject AV. They rhetorically attach to AV terms like fair/unfair, or simple/complex, that sound pleasant or unpleasant to most people. Perhaps if they argued more honestly, for example “vote for AV because it helps us, and we are better than those other parties for these reasons”, supporters of those other parties would take the point and vote against. The result is people think that voting for an electoral change is not about policy and governments, but about the particular aesthetics of voting.

What does a voting system do? It produces governments. So the question is: 
Is AV likely to lead to better or worse governments being elected? 
In reality the AV vote is about exactly the same issues that you vote for in a normal election: policies and governments. But it’s more difficult because we have to try and guess what the effects will be on policies and governments, which is not easy to work out. 
So if you think submitting a vote under AV is complex, or tactics in FPTP are difficult, the vote on whether to vote for AV is much harder. But we’ll try to make some sense of it.

The effects of AV
A voting change produces two effects:

  1. A direct effect: Given existing parties and their positions, how will the voting scheme change which party gets chosen?
  2. An indirect effect: this incorporates how parties adjust to the new system.
(This is a tautology, but it can split up the problem usefully.)

The indirect effect is much harder to gauge, and I don’t know that anyone has much idea of what it will be. Would new parties form and succeed under AV that would not under the FPTP? How will parties adjust their policies and tactics if AV comes in? 
I don’t have any strong view that these effects will change policy in any particular direction. So I’m going to look at the direct effect. The main parties and the published analysis seem to be taking the same line and assuming the direct effect is the important one here.

The direct effect
      1) Who will gain and lose MPs?
In the short term, probably parties won’t adjust to the change immediately. So the direct effect is likely to dominate.
  • To estimate this, some people have done simulations based on survey data. These seem to indicate Labour and the Liberal democrats will gain, and the Conservatives will lose from AV.
    • See http://www.oxfordjournals.org/our_journals/parlij/gsq042.pdf
    • See also http://news.bbc.co.uk/1/hi/uk_politics/8506306.stm 
  • This is consonant with the actual positions of parties: Liberal democrats strongly for AV, Labor mostly for, including the leadership, Conservatives solidly against. Presumably, they have paid consultants to analyze the question and we can rely on their supporting the position that is in their self-interest.
So who gains and loses? Liberal democrats gain almost certainly; conservatives lose probably; Labour gains (slightly less) probably.
Overall there is probably a shift to the left with AV.
      2) Majority governments
This is an easier observation, and is a consensus about AV. AV increases the likelihood of a hung parliament, where no party has a majority; so it increases the chance of coalition governments.

Is this good or bad?
  • Minority and coalition governments
These are much less likely than majority governments to have the stability and internal relationships needed to govern effectively. This is a common informed opinion about political systems in the world. But importantly, and this is the key argument for me, the people who stake their money on this question are confident that this is the answer. 

The stock markets move on the assumption that this is true. Stocks fall if a hung parliament becomes likely. This is reported in the media whenever an indecisive outcome is likely. The effect is independent of policy positioning, with markets typically preferring a center-right majority to a center-left majority to a hung parliament. 

As measured by competence of a new government to manage the economy, the lack of a straight majority is bad (probabilistically speaking). The risk that ideologically very different groups will not be able to work together is a significant problem here.
  • A move to the left
It’s harder to persuade people on a big question like this if they don’t already agree, but I believe this is the wrong direction to move and here are my reasons. Let me concentrate on the economics here. Left wing economic policy:
    • Reduces incentives to work and invest. This is the consequence of the large taxation and redistribution system that is in place. It should be reduced in scope and not increased.
      • The aim is to reduce relative poverty, but it is a burden on the activity of the private sector, including the many aims that people set for themselves, and also reduces total economic output. It also reduces the link between actions and their consequences, and leads to a dehumanizing dependence on the state.
    • Overregulates business. Labour markets are particularly overregulated, with restrictions on firing, discrimination law, health and safety regulation, etc.. Firms will be risk-averse in hiring and unable to contract with completely flexible wages, causing frictions between supply and demand, i.e. unemployment. Some regulation is necessary for trust but current regulation goes far beyond that.
    • Distrusts market solutions, believing instead in direct control of certain services. But markets can price goods and allocate them efficiently. Government is limited in knowledge and constrained by ideological and institutional factors.
      • Suppose a government were in charge of the automobile industry and distribution of cars. Then it would ensure that everyone’s car is of the same quality. Anyone can see that is nonsense, particularly for the poor, who would want to sell theirs and buy a cheaper one, and rich, who would want to sell theirs and buy a more expensive one.
      • But this is exactly what the government does in healthcare and education.
    • Will become increasingly costly in a competitive and globalizing world. This world is not dangerous; people will still be able to work and make a living. But the ability to survive by transfers from wealthier people will be reduced as people and businesses can relocate if they face high taxes.
Moving from FPTP to AV increases the risk of hung parliaments, with their likelihood of producing governments that are less able to govern effectively. It also seems to favour left-wing parties, which I believe will lead to inferior economic policy.

Monday, 11 April 2011

The ICB interim report: leaving us in a dangerous situation.

April 11th has for months been a significant date in the diaries of bankers. This morning the Independent Commission on Banking (ICB) released its interim report, a sort of preview of the final recommendations it will present to the government in September with the aim to improve stability and competition in UK banking. 

It was not just the banking sector eagerly anticipating todays report, I have been excited about it for weeks(!), and have thoroughly enjoyed a day in a warm and sweaty office reading the report in detail with the Positive Money team.

After threats that the banks will pack up and leave the UK*, and cries that the commission's recommendations would destroy profits, meaning that nationalised RBS and Lloyds might sell at a loss to the tax payer, the markets proved optimistic this morning in response to the report as shares in Barclays, RBS and Lloyds rose by 3.28%, 2.49%, and 0.72%, respectively. Unfortunately for the public, the outcome of the market is not determined by investors with long term outlooks aligned with the welfare of society, and in contrast to the banks, our evaluation of the report was critical. 

I just want to remind you how important the influence this commission has on the government to reform the banking sector is. In the words of the commission...
" The UK was severely affected by the crisis. National output in 2010 was 4.5% below its pre-recession peak. Unemployment has risen by more than 800,000 since 2007. The  public finances have deteriorated sharply, and the 2009/10 deficit exceeded 10% GDP. There is evidence to suggest that some of the output loss economies suffer during crises is permanent. Work by the Basel Committee on Banking Supervision suggests that the cost of banking crises may exceed 60% of pre-crisis GDP. More than 80% of RBS and more than 40% of Lloyds are in state ownership as a result of the Government bail-out of the banking system."
So what does the ICB propose? 
1) Increased Competition
Competition was part of the commission's remit, and so had to be addressed. Indeed, increasing competitive pressures in the UK banking sector, which is concentrated in the hands of The Big Four (RBS, HSBC, Barclays and Lloyds TSB) is no bad thing. If we suspect that a lack of competition is allowing these firms to keep costs up, then increasing competition promises to benefit consumers by decreasing the cost of borrowing and increasing returns on savings. Providing information to help consumers choose the best bank for them, another proposal, is of course also welcome. These proposals, however, are fairly irrelevant to dealing with a financial crisis.

Crucially, the report does not address the unique lack of competitive pressure that the banking sector faces as a whole. The government promises to insure all deposits up to the value of £50,000 should a bank fail to repay a saver, and we have seen that the government bails out failing banks at huge cost to the tax payer. The possibility of external support boosts banks ratings by the ratings agencies at no cost to themselves. Haldane (2010) estimates that the government guarantee reduced bank funding costs by £57bn per year from 2007-2009. No other industry or service sector receives this kind of support, or subsidy, which fundamentally buffers it from true competitive pressures. When any other firm goes bankrupt they exit the market leaving more room for companies with the best skills and ideas to grow. The result is that banks can behave recklessly by taking on excessive risk; if they are lucky they will make high returns, and if they mess up they know that the government will help out.

2) Increased Capital Requirements

In their analysis of the recent crisis, the report describes the "explosion of leverage" in the run up to the crisis as key to explaining why the banks were so vulnerable. Just before the crisis banks lent up to 50 times the amount of capital they actually had! Increased capital requirements are being called for internationally by regulatory bodies to reduce the extent of leverage banks can take on, and reduce how hard they can fall in a crisis. Specifically, the report suggests that retail banks hold capital equal to 10% of their loans and investments, and that wholesale banks should meet the slightly lower capital requirement of 7% (in line with the Basel III accord). I think the most we can say is that these small adjustments might make the banking system slightly "less brittle"; the commission estimates that it "would allow total assets [in the wholesale banks] to be almost 30 times equity capital. And so banks could only withstand a 3.5% fall in the value of their assets before wiping out this capital." 

This leaves their final proposal to make the banking system more stable...

3) Ring-fencing

The idea behind ring-fencing is to stop risky investment activities from pulling down the retail activities (where you and I hold out current accounts) of banks by ensuring that they are each supported by their own separate pools of capital. The separation has been described as a firewall because it is not permanent, it is only activated in times of need, and only if it does not pull down the other part of the bank down too. Ben Curtis from Positive Money explains it well in a piece he wrote for Liberal Conspiracy today: "The two arms of the bank would to still be able to bail each other out in difficult times, but neither would be able to bring the other half down in a crisis."

Firstly, this proposal demands more from the regulators than they have shown to be capable of (the regulators embarrassingly failed to foresee the recent crisis): how will they know when the special circumstances in which the firewalls need to be activated hold? Secondly, because of a lack of information and transparency regulators will have to rely on what the banks tell them. This means that should the retail activities of a bank go under, the bank manager has an incentive to tell the government that their investment arm is not strong enough to bail it out. The government will then be likely to bail out the failing retail activities, and the bank's investment activities will be protected at a cost to the tax payer. Thirdly, the commission mention that even if banking crises can be contained to certain arms of bank activities, the market response could be so negative that the crisis could spread to other areas.

I listened with great esteem to Liam Halligan's damning crtique of the report on PM (radio 4). (He is currently chief economist at Prosperity Capital Management, and a highly regarded financial journalist.) He describes the ring-fencing proposal as an elegant political compromise, when what we need is leadership to get us out of a dangerous situation. You can listen here (from about 18 mins).

In sum, the commission's report provides a disappointing preview of a selection of weak and ineffective recommendations that they will make in September. I think the report betrays a bias towards the banks and the status quo, and also an ignorance by not taking seriously more 'radical' proposals. Oh, but that is for another post... I'm sleepy xx

* There is an interesting table on p.202 of the report that breaks down the amount of tax we would lose should banks move their operations from the UK, as some threaten to. Of the total £55bn the government received in taxes in 2009/10, the commission estimates that only £3bn face the "lowest hurdle to departure" and that £30 - 36 bn would be "hard-to-impossible to leave". Should we be so concerned by their threats?

UPDATE: You can watch Ben Dyson's summary of Positive Money's reading of the ICB report here.

Saturday, 2 April 2011

The Alternative Vote #3: The Benefits of AV

A piece by an Economics DPhil student at Nuffield College, Oxford University, who is volunteering for the Yes Campaign.

Why should we adopt AV?  The current voting system is broken.  
  • IPPR research shows that the last election was decided by 1.6% of voters in marginal constituencies.  
  • Polling indicates that 19% of voters have found themselves voting tactically.  
  • At the last election, less than 1/3 of MPs got the support of a majority of their constituents and around a quarter of voters voted for candidates who were neither winners nor runners up.
  • Turnout has fallen lower than 60% and, across constituencies, has been negatively correlated with the size of MP’s majorities (see graph).  

These are not the signs of a healthy democracy.

AV will represent a dramatic improvement.  Under AV voters give more information.  Rather than putting a mark beside the name of one candidate, they rank the candidates putting a ‘1’ next to their first choice, ‘2’ next to their second choice and so on.  The election then proceeds through a series of rounds, at the end of each round the candidate with the least votes is eliminated.  In each round of the election your ballot paper counts as a vote for your most preferred candidate who has not yet been eliminated.  The process ends when one candidate has achieved 50% of the vote.
  • MPs will have to get the support of a majority of their constituents. 
  • Many seats will become a lot more competitive ensuring politicians have to pay attention to more voters than those who live in a handful of “key marginals”.  
  • AV will practically eliminate the incentive to vote tactically, allowing voters to support their best candidate without risk of gifting the seat to their worst candidate.  
  • By making more constituencies more competitive, it will increase the incentive to vote and help to boost turnout.

The main argument against electoral reform being used by the No campaign is the kind of lie that would make Phil Woolas blush!  They claim it is too expensive.  I won’t repeat their figure as this line of argument is an exercise in repeating a lie so many times that it becomes true.  However, it is worth remembering three things:
  • 52% of their cost figure comes from new voting machines.  There won’t be any new voting machines.  AV can and will be counted by hand – that’s what they’ve been doing in Australia since 1919.
  • 37% of their cost figure comes from the cost of the referendum itself.  That won’t be refunded in the event of a no vote.
  • What is left of their initial figure for the “one-off” cost of AV is 22% of the regular cost of holding an election.  As far as I’m aware, the No campaign haven’t suggested cancelling elections because they’re too expensive...  yet.

    The Alternative Vote is a small, simple, smart change that will make a big difference to improve our democracy.  MPs will have to reach beyond their traditional support in order to get elected.  The culture of jobs for life that has made MPs so complacent will be brought to an end.  The number of safe seats will fall and political parties will have to pay attention to the needs of more of the country rather than a few key marginals.  We must seize this once in a generation chance to reform our voting system and reinvigorate our democracy.