## Some post-referendum consolations

I started my first post on AV by saying that I had yearned for a better voting system all my life but that I expected to be disappointed. Now the expected disappointment has arrived, and although the count is not yet finished it is already clear that the referendum is a massive defeat for AV [update: by approximately 70% to 30%]. Moreover, the consensus is that the opportunity will not arise again for at least generation. By then I’ll be an old man, so even if we do eventually get a decent voting system I probably won’t live to see how it affects politics in this country.

It is not easy to say anything positive about this situation. But let me try all the same.

The prospects for voting reform.

Is it true that we will have to wait at least twenty-five years for another chance to change the voting system? It certainly could be, but it is not an absolute certainty. It does of course seem as though the conjunction of circumstances that led to the referendum we have just had is unlikely to happen again any time soon, since if the Lib Dems see their representation in parliament drop drastically, as is likely, then the number of seats going to Labour and the Conservatives will have to be that much more equal for there to be any prospect of the Lib Dems being able to negotiate for voting reform again.

And even if, by some miracle, the Lib Dems found themselves holding the balance of power at the next election (which might just happen if, say, the Conservatives are deeply unpopular, but the new seat boundaries give them some extra seats and Ed Miliband lacks the charisma to capitalize all that much on their unpopularity), it seems very unlikely that they would try to get another referendum on voting reform in the ensuing negotiations: it would be far too easy for opponents to say that the public had made its decision. In fact, this is such a strong argument that I think one would have to be delusional to hope for voting reform in either this parliament (well, that much is too obvious to be worth saying) or the next.

Indeed, the Lib Dem route to voting reform looks as though it might be doomed for ever, unless there is a major change in attitudes in this country. Consider what it requires: first the Lib Dems have to hold the balance of power; then they have to enter into some kind of agreement with a major party, in a country that regards compromise as betrayal (a charge that has some substance in this case but that would I think be applied to any agreement); and then they somehow have to have a referendum that is not regarded by many as a referendum on the coalition itself, in the face of campaigners who will be encouraging just that. It doesn’t feel as though it could possibly happen.

A much more plausible route to voting reform is through the Labour party. They have made noises about it in the past, and although their MPs were mostly opposed to AV, the younger generation of Labour MPs seemed more in favour than the old guard. (This was certainly the case amongst those whose views were reported in the media: I don’t know whether it applies to the rank and file.) But there is always the problem that when a party gains power under FPTP with enough of a mandate to make a major constitutional change, it is in a position where any change is likely to weaken its position, at least in the short to medium term.

So perhaps the best hope for voting reform in the next parliament but one is that the Conservatives win a comfortable majority at the next election, but that Labour win a significantly larger percentage of the vote. In fact, here is a suggestion: vote tactically at the next election to make this happen.

How does one do that? Well, in any seat that Labour isn’t going to win, we want to maximize the Labour vote. And in any seat that Labour is going to win, we also want to maximize the Labour vote. Does this mean I’m saying that everyone should vote Labour? No — if you are in a marginal constituency where Labour is a serious contender, you should vote against Labour (or, better still, just enough people should vote against Labour for their main rivals, probably the Conservatives, to squeak in). The result of all this would be to maximize the Labour vote without giving them seats, leaving them with the feeling of burning injustice that Lib Dems have had to put up with for decades.

This is of course pure fantasy: I do not seriously imagine that many people will be persuaded to use their vote tactically for the sake of (possibly but by no means definitely) advancing the cause of voting reform when there are much more immediate causes such as the economy, education and health to worry about. But if the Conservatives choose the new constituency boundaries cleverly enough, they may help to create a manifestly unjust result and thereby inadvertently bring forward the day when voting reform is next considered seriously. (By the way, I think it is wrong to describe the reduction in the number of constituencies as gerrymandering. The current unequal constituency sizes give an unfair advantage to Labour, and I don’t see that removing that unfair advantage constitutes gerrymandering. It’s more like the opposite. Of course, it will become gerrymandering if the new boundaries are drawn up specifically with a view to maximizing the number of Conservative seats, and I don’t have 100% faith that that will not happen …)

Looking further ahead, it is said that younger people are more in favour of voting reform. (As one commenter suggested, perhaps votes should have been weighted according to how many general elections the voter is likely to get to vote in.) Unless they gradually morph into FPTP supporters as they get older (perhaps because they get more right wing), this gives some hope that if the question does come up again in a generation’s time then there will be more chance of a change. Also, one lesson from the current referendum is that there is almost certainly no point in trying to introduce the “miserable little compromise” of AV (which I have argued is not all that miserable). The arguments for PR are much easier to make, so any future attempt will almost certainly have to be for full-blown PR.

Incidentally, on the subject of slightly off-beam suggestions for voting reform, another amusing one is that each constituency should select its MP by whatever procedure it likes. So if you’re in a constituency where most people would like a runoff system, you have a local referendum, get your system up and running, and use that to select your MP. But if you’re in an FPTP-ish area then you can use that. What could be more democratic than letting each constituency decide how it wants to select its MP, rather than imposing a uniform system on everyone? This idea does raise a problem though: how does a constituency decide what voting system to adopt? Presumably it votes. But according to what system? (I think even the most ardent FPTP supporter should recognise that using FPTP to decide amongst four or five voting systems would be idiotic.)

What if we’re stuck with FPTP for the next 50 years?

So far my “consolations” have consisted in wildly optimistic fantasizing. So I’ll try to be more realistic. Let’s assume that we’re not going to get voting reform any time soon. How bad is that?

If you support voting reform because you support the Lib Dems, or more generally you want to put an end to the Labour/Tory hegemony and usher in a new kind of consensual politics where issues are debated on their merits, then it is pretty bad. But what if what really interests you is not who has the power but what decisions get made? Then the situation is more complex. I’ll illustrate that with a couple of examples.

Example 1. The Labour/SDP split.

The SDP split from Labour in 1981, formed an alliance with the Liberals, and, as I have said already, never managed to get more than a handful of seats despite getting a significant proportion of the vote. The reason they split was that they regarded Labour as too left wing, a statement that became all the truer once they had left the party.

Now one view is that the whole project was a failure: the SDP never came close to being able to implement its policies. But another view is that they forced Labour to move to the centre, since to do anything else was to risk permanent Tory rule as a result of the split of the left into left left and centre left. And in 1997 we got Blair, who was centrist enough that, had he (or rather someone like him) been leader in 1981 there would have been no need for the SDP. So one could argue, and people have argued, that the SDP got what it wanted — it just did so indirectly rather than directly.

I’m not saying that’s an ideal state of affairs, since it did take them sixteen years and during those sixteen years we got hit with some awful decisions such as the poll tax and rail privatization. But it does at least illustrate the (not altogether surprising) principle that a party can have a significant influence on the decisions taken by government, even if it does not form part of that government.

Example 2. Welfare reform.

My second example is of a policy that I have supported ever since a few seconds after I first heard of it as a teenager: negative income tax. The few seconds were what it took to move from thinking it was obviously nutty to understanding the reasoning behind it. Actually, negative income tax is not the whole of the story. Another major part is the integration of the tax and benefits systems. I’ll just say a little bit about these issues before going back to the general point.

Poverty traps have long been recognised as a serious problem in the UK. If you are on benefits, then those benefits are withdrawn when you earn money. At the moment, they are withdrawn at rates that mean that many people find that for each pound they earn, they end up better off by only a very small amount such as 15p. In fact, some people end up worse off if they work, when all the expenses (such as childcare) are taken into account. Something is very clearly wrong with an economic system that for many people provides no incentive to work.

Now suppose that you were designing a system from scratch. (A major problem with what I’m about to say, and with welfare reform in general, is that one is not designing a system from scratch. To keep the discussion simple I will make this assumption, but ultimately one needs to work out a way of moving from one system to another without causing massive hardship and discontent, and this makes it formidably difficult to implement change.) If you were a mathematician, then you would probably consider the following simple model, at least to start with. You would like to choose a function $T$ (for take-home pay) where the input is the amount you actually earn — let’s call that $A$ (for actual pay) — and $T(A)$ is the amount you end up with after the tax and benefits system has had its way with you. In deciding what the function $T$ should be, you would take into account the revenue the government needs, the distribution of how much people earn (and how it might change if poverty traps were eliminated), and political considerations such as how much you want to redistribute from rich to poor, the effect of tax on incentives to work, and so on.

One obvious point is that if somebody is actually earning nothing — they might, for instance, be unemployed — then we do not want them out on the streets. So we want their take-home pay to be non-zero. That is, $T(0)$ should not be zero, and more generally if $A$ is very small, then $T(A)$ should be greater than $A.$ If we were to merge the tax and benefits system and call everything tax, then the obvious definition of the “tax” you pay, if your actual earnings are $A$ and your take-home pay is $T(A),$ is $A-T(A).$ So if $A$ is small, your tax rate is negative.

The idea of a negative tax rate sounds ridiculous until one thinks (i) that it is just giving a different name to benefits, (ii) if you do it properly, you can choose the function $T$ in such a way that everyone has a reasonable incentive to work, and (iii) it is only the very poorest in society who end up with more money than they earn. The necessary condition for (ii) is that the derivative of $T$ should be bounded below by a reasonably large lower bound. In more everyday language, you want a system where, especially at the lower end of the scale, for every pound you earn you get to keep a significant percentage. (I would suggest that you should get to keep at least 60p, the amount you get to keep as a higher-rate tax payer under the current system. Indeed, in an ideal world the derivative would not just be bounded below but monotone decreasing, though whether that is practical I don’t know.)

Further mildly consoling thoughts.

I don’t have much to say here. The first thought is that if it is correct that there is absolutely no chance of voting reform for at least ten years, then we can at least say that in the next election AV would probably have made very little difference. Why? Because the Lib Dems are likely to see a collapse in their share of the vote, so we’ll be back to something like a two-party system for a while. And under a two-party system FPTP isn’t as bad as it is when there is a biggish third party.

On the topic of the Lib Dems, I think they should be very worried not just about the short term but about the long term as well. Plenty of people are angry with them, and in the short term that will be disastrous for them. But in the longer term people are going to ask themselves the following killer question. If the Lib Dems are going to do a deal with Labour or the Tories in the event of a hung parliament, then what is the point of voting Lib Dem? Surely one should just make one’s mind up which one prefers out of Labour and the Tories rather than leaving the decision to somebody else and to the unpredictable results of coalition negotiations. It will be very hard for them to come up with a convincing answer to this: having good policies is, alas, not enough.

Another thought is that if, as many predict, the newspaper industry does not manage to survive in its current form because of the internet, then perhaps the concentration of power in the hands of people like Rupert Murdoch will be lessened. Perhaps within ten to twenty years we will see major changes to how opinions are disseminated that will mean that no single person has as much influence as the most influential people today. I don’t know whether that would be good for democracy, but improving on what we have now ought not to be hard.

How to get AV even if the system is officially FPTP.

An apparent disadvantage of such an endeavour is that if it was successful then it would make it very hard for small parties to grow (as for tactical reasons people would not vote for them). But if there was enough local polling, where the question was not, “Who will you vote for?” but “Who would you choose if the decision was yours and yours alone?” then people would have an opportunity to express their opinion and help choose between the main candidates — exactly what AV allows you to do.

In general, what I am saying here is that there are ways of dealing with the deficiencies of FPTP even if we are stuck with FPTP. It would require the tactical-voting movement to expand greatly. It is unlikely that enough people care enough for this to happen, but the theoretical possibility exists, and making it a practical one is much easier (though still difficult) now that we have the internet.

Let me sum up my suggestions here.

1. Have a website with as much constituency-by-constituency information to enable almost everybody to determine which are the two leading candidates.

2. In cases where the second and third candidates are neck and neck, do more sophisticated polling to see which would do better in a two-way contest, declare that candidate to be the leading one, and make that information available on the website.

3. Do constituency-by-constituency polling where the question is, “Which candidate would you choose if the decision were entirely up to you?” Publicize this information as much as possible, especially in constituencies where it appears that a different candidate would have won if everybody had voted for their actual favourite candidate.

4. Encourage people to vote for one of the two leading candidates while at the same time registering on the website and informing it which candidate they would have voted for if the decision was entirely theirs. This is supposed to be a substitute for putting candidates in order of preference under AV: if your first preference is for a candidate who is unlikely to win, you give that information to the website rather than wasting it in the ballot box. Tactical voting might become more popular if there were a widely recognised way of expressing your true feelings.

A system like that would give people the chance to vote in the expressive way that AV allows. The idea comes off the top of my head, and could probably be improved. (There is no reason, for instance, why one couldn’t collect information about which candidates would have done well under range voting.)

Incidentally, if you want something closer to PR rather than AV, then you have to go further and indulge in vote swapping. For instance, if you support Labour in a seat where the Lib Dems are second, you find a Lib Dem supporter in a seat where Labour is second, and agree that you will vote Lib Dem if they vote Labour. This has happened to a small extent, but is harder to organize (since nobody knows if you have kept your side of the bargain) than the suggestions just outlined.

So if you are very disappointed, or even angry, about the result of the referendum, why not do what you can to create a more AV-like voting culture from within the confines of FPTP?

One final, really quite big, consolation: Cambridge voted yes (by 21,253 votes to 17,871).

Update. Here is a list of the ten places in the country that voted yes: Cambridge, Camden, Edinburgh Central, Glasgow Kelvin, Hackney, Haringey, Islington, Lambeth, Oxford, Southwark. If you’re not from this country, I should explain that the places that aren’t Oxford, Cambridge, Glasgow or Edinburgh are districts of central London. For more details see here. There are remarks it is tempting to make, but I’d better not.

### 46 Responses to “Some post-referendum consolations”

1. László Says:

Illuminating thoughts. I think you’d also like other very serious proposals coming from a bunch of (idealistic? pragmatic?) experts: http://www.ifs.org.uk/mirrleesReview (all chapters of both volumes freely available)

Thanks for paying attention to us public economists! We do make sense. 🙂

I wonder if you had a chance of looking into recent arguments or Eric Maskin on “How to Elect Presidents?” (and other eternal social choice issues). I am glad to see that these issues are fascinating for mathematicians too.

But first things first: RIP AV…

• gowers Says:

Just after Jim Mirrlees won the Nobel Prize in economics, he gave a talk in Trinity College about his work, which I attended. I don’t remember much of it, but I do remember that one of the questions he looked at was how to maximize the tax revenue, given certain requirements of the tax rates. (I also remember that he used a static model.) And I also remember, I think, that if maximizing the tax revenue is the only concern of the government, then it is not the case that the marginal tax rates should increase with income. If true, that is an interesting case where what is in people’s financial interests would be politically impossible to get through.

• László Says:

To Tim: The whole approach of optimal taxation might be naive or idealistic (esp. from a cynical view of politics) but it is not that pointless. Usually the government needs to raise some revenue, for whatever purpose, and given that constraint, people’s responses to taxes, the distribution of their earnings capacity, and some weighting of their utility, social welfare is maximized by an optimal share of the burden. Very often you can marginal tax rates falling at some points of the income distribution, but that need not mean falling average tax rates (regressivity). And in any case, voters already OK with falling MTRs todays — with all the phaseouts and other quirks (as you also noted), it is commonplace.

E.g. a great insight gleaming from the formulae are that you can tax the rich more not only because they need the money less but also because their 1% of income can pay for not taxing away 1% of many-many poor people’s income. Etc.

I think you and your readers might enjoy the approach and thoroughness of the Review linked in my original comment, but for less applied (to the UK, of all places!) results, you and they can also check these little accessible review pieces.
http://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.24.3.183
http://pubs.aeaweb.org/doi/pdf/10.1257/jep.23.4.147

If you are interested, of course, most of the original literature would be accessible to you and them too, in any case, so you might appreciate, say, the recent works of Emmanuel Saez, Raj Chetty, or Emmanuel Farhi:
http://elsa.berkeley.edu/~saez/
http://obs.rc.fas.harvard.edu/chetty/index.html
http://www.economics.harvard.edu/faculty/farhi/papers_farhi

2. Jonathan Phillips Says:

I already am an old man. I’ve been voting Liberal since 1966. Last year, for the first time, I voted for the winning candidate and got a Lib Dem MP (on less than 30%, but so what?), and the Lib Dems had a position of power nationally. Clegg has thrown it all away: he has not only wrecked the Lib Dems now and for the foreseeable future, he has also ruined any prospect of electoral reform. Everything he has touched has turned to cr*p.

Does anybody else have the feeling that the Cameron-Clegg deal was a stitch-up? – that they’d already reached a contingency agreement before the election? Five days is a very short time to reach an agreement on government – they take longer in countries that are used to coalitions, even when the parties’ preferred partners are known before the election (Ireland, Germany).

Here’s a horrifying thought. Salmond gets his way, Scotland leaves the UK, and the rest of us get Tory governments till the end of time. Or at least the end of my lifetime.

And an entertaining thought: the PR system devised for Scotland was intended to prevent any one party gaining an overall majority. Best laid plans and all that.

Over and out.

3. Gil Kalai Says:

Tim, wouldnt a strong form of consolation from the point of view of an AV supporter would be something like this:

“We had, for the first time in our history an opportunity to examine our voting system against an alternative voting system. The decision was taken in a most democratic way by a referendum. For several months both supporter and objectors had an opportunity to make their arguments. The outcomes were decisive – with 2:1 margin the voters rejected the alternative. Apparently, the collective wisdom of the voters gives much more weight to the concerns from the new system than to its possible advantages.”

• gowers Says:

I might go along with that if I believed that most voters had thought carefully about voting reform and had concluded that the drawbacks outweighed the merits. But I’ve read so many comments on various blogs from people who have said that they were going to vote no to express their anger against the Liberal Democrats (in other words, using the referendum for a different purpose) and seen so many wrong arguments being put forward and apparently widely accepted, that I do not find it a consolation at all.

To put it another way, I think that if a referendum had happened at a random moment over the last ten years and had not been associated in the public mind with unpopular coalition negotiations, then the result might have been different — not very long ago, polls were showing a clear majority for reform.

• Anonymous Says:

Prof. Gowers, if you think the voters fools for having rejected AV, why do you urge that the preferences of those same fools be more fully reflected in election results?

• gowers Says:

First off, I wouldn’t go as far as to say that they are fools. However, your question is an interesting one — it is certainly possible in my view for the majority of a population, even a large majority, to be wrong about something. And I think that the tools of modern advertising make it happen quite frequently. And I’m confident that if we had full PR in this country, then the voters would often make choices that I didn’t like. But the obvious systems for dealing with that problem, such as leaving decisions to experts, are not merely morally repugnant but are also so full of practical difficulties as not to be worth thinking about.

• gowers Says:

It feels a bit strange to do this, but let me elaborate on why I wouldn’t say that people who voted no were fools. I think large numbers of people who voted no reasoned that a yes vote would principally help the Lib Dems and they were angry with the Lib Dems. And although I regret that, they had a perfect right to do it, it was a rational decision to make, and foolish is not the right word to describe it. I also think that people who reasoned like this had very little motivation to examine the true arguments in favour of and against AV, so if they believed some of the no campaign’s falsehoods, it wasn’t a sign of lack of intelligence — just lack of any reason to bother to think critically about what they were being told.

• Gil Kalai Says:

It is an interesting question to what extent the outcomes were influenced by anti LIB Dem sentiments (rather than simply prefering the old voting system). Looking at polls, it looks that a few months ago perhaps as late as January/February the polls showed euality between yes/no voters and even some advantage for the yes camp. Were there things that Lib Dem did in the last three months that could antagonize voters?

Actually this brings to mind another tactical matter for an AV voter. Suppose that you are a voter that either prefers that Lib Dem form a government or that Lib Dem comes second in your preferences. However, you prefer that there will be a government formed by either Labour or Conservatives on their own on a coalition government like the present one where Lib Dem is a minor partner. Then to prevent a hung parliament you may still rank Lib Dem third.

• Gil Kalai Says:

One thing that I am puzzled about is this. Lib Dem was the clear potential winner from a yes decision: AV improves the situation for the third largest party, it also improves the situation for a politically central party, and it was also an initiative of the lib dem to start with so a success will give them some political revenues.

Under these circumstences the Lib Dem strategy should have been to give the Labour leaders (which fortunately for them supported AV) the driver sit in campeigning and promoting this reform at all possible cost (including self humiliation).

In reality it seems that this was not the Lib Dem strategy and even a joint Labour-Lib-Dem rally in support of AV in March (when the results were still unclear) was cancelled.

• Anonymous Says:

Perhaps I shouldn’t have phrased my question so sharply; these things are best discussed in very understated language. I intended to raise the problem of individual rationality within the context of the AV vs FPTP problem. This problem is quite distinct from the purely Arrovian problem of irrational decisions by a group composed of rational individuals that has been discussed so thoroughly on this blog. This problem itself has many subproblems. For example, I don’t think it quite works to require that a voter simply apply his ordinal utility function (or partial function) U to the parties and record the output. I gather that there’s empirical evidence that U isn’t even well defined, in the sense that it depends quite strongly on how its inputs are represented.

Furthermore, AV may be substantially harder to use than FPTP. Not harder to understand, harder to use. That is because political parties are highly multidimensional objects that can’t be ranked in strict linear order without making a lot of difficult or even arbitrary choices. People vary greatly in their ability to make such choices. So I suspect that AV really is harder for many voters than FPTP, which really requires only that a voter choose one preferred party. Voters can solve this problem in various ways, such as voting for one party (in which case AV reduces to FPTP), voting for two parties, or rating many parties despite having very incomplete or biased information about them. I could elaborate further on this issue but I won’t.
F

• Travis Says:

Democracy is the theory that the common people know what they want, and deserve to get it good and hard.
– Mencken

4. Peter McNamara Says:

Is there any reason that voting reform has to be accomplished through a referendum, rather than say an act of parliament?

I’m unfamiliar with the British system, but I assume that it was the latter route that got a preferential system setup in Australia. The conservative parties were unhappy with the situation of a 1918 by-election where Labor won with 34.4% of the vote against a large conservative vote that was split and changed the system.

69% is a very depressing result. Its hard to get a yes vote at any referendum without some sort of bipartisan support.

• Richard Baron Says:

Parliament can do pretty much what it likes (there are European law complications in relation to some matters, but Parliament could decide to quit the EU). The changes in the franchise from 1832 onwards were all made by Parliament, without formally asking the people what they thought.

So an Act of Parliament would be necessary to change the voting system, and a referendum was entirely optional. Parliament could even pass legislation that would automatically implement the result of a referendum (as it did – sections 8 and 9 of the Parliamentary Voting System and Constituencies Act 2011), then look at the result, immediately change its mind and pass new legislation that would do the opposite.

It is just that these days, if you are going to change the method by which one house of the legislature is elected, it looks polite to ask the electorate. And of course, the LibDems would have got an instant no in a House of Commons vote. Their only chance of a yes was to ask the electorate, so a referendum had to be part of the coalition agreement.

5. bobchew Says:

Thanks Prof Gowers for this and its related posts. Being a non-professional mathematician and unable to comprehend most of your other postings, these ones demonstrate to me why mathematicians should play a more significant role in public policy. It will bring more sense to the discussion and guide us to better decision making (assuming people do treasure rational thinking).

I live in Singapore. We are right now in the midst of polling day. Our system is like the British – FPTP – with a major modification. This is the so called Group Representation Constituency (GRC), which comprise from 3 to 6 constituencies, which gets voted in as a group. So if you have a GRC with a weak candidate (unlikely to win) “packaged” with, say, 3 other strong candidates (likely to win), then all 4 will likely get voted in.

Many say this GRC modification favours the ruling party which has a stronger slate of candidates which can help pull in the newer, lesser well and (perhaps) weaker candidates.

No one has done the analysis for FPTP vs FPTP (w GRC) in the way you did for AV vs FPTP. But the layman’s view here is that this makes it hard for new parties with smaller number of candidates to succeed.

In Canada, we just had a federal election, where the Conservatives won with 40% of the popular vote, despite the other 60% voting for essentially center-left or left parties. We hoped (in vain) that the UK voting reforms would pass, and one day spread to other commonwealth nations.

However, I’d like to point out that we did have websites very close to the ones you describe. The main site: http://www.projectdemocracy.ca/ analyzed polls and advised the left on how to vote to defeat the conservatives. (This included more detailed polling for critical ridings.) That site also suggested, in appropriate situations, that voters swap their votes with people in other ridings, with the aim of voting strategically without sacrificing the percentage support of the smaller parties: this was facilitate by another website: http://www.votepair.ca/swap-exchange/.

7. Richard Baron Says:

On the practicalities of the function T, pretty much any function you want should be administratively feasible, if you adopt and extend the central deduction system that the Government mooted last year, but away from which it has since backed. The idea would be that everything that would count as part of A would flow through a specified bank account with your name on it. (The Government only thought about doing this for your employment income.) Then the state could subtract [ A – T(A) ] each week or month, so as to yield the desired result.

The Government backed away from the idea because many (not all) people were outraged at the idea of money flowing, not directly from employer to employee, but via an account into which the Revenue could put its sticky paw. But it does look as though we are going to get real-time information, under which the information on each employee’s payslip will go to the Revenue each payday. (It is a little-known fact that under the current PAYE system, employers only send aggregate information each month, and the breakdown by employee only after the end of the year.) A move to real-time information will widen the range of T functions that it would be practical to use.

The real problem is affordability. The higher the lower bound on the derivative of T, the more it costs, and the further up the income scale people are receiving negative tax rather than paying tax. Motivating people individually to get off benefits costs a lot in aggregate benefits. But we could surely make some progress by getting rid of some of the kinks in the current implied T which produce high benefit withdrawal rates, and having something rather smoother. Thinking in terms of a single function is in itself a very useful way to improve the formulation of policy.

Mirrlees and maximising revenue have come up in the comments. One of the nicest results in this area was given in “A contribution to the theory of taxation” by F P Ramsey, philosopher (hurrah!) and mathematician, in 1927. The problem was to raise a given amount of revenue by taxing different types of spending, while minimising the reduction in utility. The answer, under wholly unrealistic assumptions of the kind that one has to make in this sort of work in order to get any answers at all, is that you should tax most heavily the spending that is least sensitive to price changes. Politicians have unconsciously put this result into practice by taxing alcohol, tobacco and petrol. But they have not extended heavy excise duties to food, a certain quantity of which would still be sold even if its price doubled. And I don’t want to encourage them.

On voting reform, I entirely agree that better flows of information could make it much easier for us to achieve an approximation to the voting system that we wanted, even while the current system remained the official one. But I guess there would be interesting questions in the general area of game theory, even if everybody wanted the same unofficial voting system (and still more so if different people wanted different unofficial systems – although the range of options would be limited by our sticking to single-member constituencies). Influence over voters would be a nice complication: if you can persuade two of your family members to vote in a particular way, then you come to the vote-swap with more clout than solitary individuals. And of course, the secret ballot means that not only is there no guarantee that an agreement will be honoured. There is no way to find out whether or not it was honoured. We would have to put our faith in the empirical work which shows that we sometimes co-operate even when we know that we could not be caught if we cheated.

8. Julian Woodward Says:

A very quick thank-you for your lengthy and considered posts during this referendum process. I have linked to your posts many times during debates conducted in the walled (well, trellised) garden of Facebook. If I can say so without sounding patronising … keep up the good work!

9. Clay Shentrup Says:

What do you folks think about the idea of expatriating to get a better system? I live in San Francisco, but I’m considering eventually moving to Australia or Germany in order to get proportional representation. With a PR system, people can create new parties that use whatever kind of new experimental voting methods they like. For instance, the German Pirate Party has used Score Voting and Approval Voting, and even a bit of Condorcet (worse and more complicated than Score Voting, but massively better than IRV or Plurality) to nominate their party list, for example.

• simon Says:

isn’ it entirely irellevant how a party choses its party list? Surely if you create a new party in San Francisco you could chose your internal candidacy list however you like. if you convince the Democrats or the GOP to use another system there is no law forbidding it.
but for parliament elections this is of no relevance what so ever, bc the official system will still be used.
but under the official system in germany the pirate party is still politically unimportant because of the 5%- elections treshhold…so I really don’t see the relevance, wouldbe nice if you could explain…

I don’t really see how PR has any positiv effect on the number of parties or the formation of new parties. in this regard the UK-system seemsalot better, bc “regional” partys Plaid Cymrz, SNP and all those from north ireland are represented in westminster… which sure increases diversity and the regional voice!

after all there aren’t many more partys in Countries using PR:
see: Austria
there are only 5 parties
The peoples party (ÖVP)- a conservativ party but fairly centrist
the socialdemocrats (SPÖ)-
The freedom party (FPÖ -don’t let the name fool you they are fairly down the right wing, and even somewhat racist- the english name is due to the fact that freiheitlich has a somewhat different meaning than liberal…
The greens- i don’t think they need introduction
Alliance for the Future of Austria- which was founded by the former leader of the FPÖ, and since then has addopted somewhat liberal policies, but still has a lot of racist cr*p, and only really exists in carinthia one of the of austria. (they barely made parliament last time, and probaly won’t next time, being caught in a bank scanda)
-Note that austria doesn’t have a liberal party… (b.c. they didn’t make the 4%-barrier in austria last time)
so i don’t thinkt that PR leads to more diversity. probably to more coalitions which need not be a good thing austrial has been governed for most of the time by a grand-coaltion, (With anotable exeption 2000, when W. Schuessel comming third in the election made himself chancelor by a deal with the FPÖ (which had for the first – and so far only time) overtaken the ÖVP.
But grand coalitions aren’t very good for the country … but thats a different story and a great mathematical blog is probably not the right place for a politcal rant.

10. Daniel Thomas Says:

Cambridge voted yes and a fair number of those yes votes were won by your rather excellent post earlier on which got a lot of traction.

11. Andy JS Says:

I’m very disappointed, having voted Yes in a district which voted 76% no, one of the highest in the country. But I think the result does show that a rather dangerous gap has opened up between “the kinds of people” (I can’t think of a better phrase) who live in the 10 areas that voted yes and the rest of the country. It would be easy for that small minority to adopt a slightly contemptuous attitude towards everyone else but I think that would be a mistake. It’s right that reforms should only happen when most people are convinced of them, however frustrating that might be.

12. simon Says:

oh just that no misconceptions a rise. I am not defending FPTP, but PR has it’s flaws to and I am not convinced that encouraged people to express their real preferences, at least not if you have an election treshold (Which all countries i know of have).

prof gowers has convinced me in his great blog post series that probably AV is the best system to get voters to express their real preference -which after all elections are there for.
(Why PR- does not always do this see below)
Thanks for all the hard work that went into writing those posts.

A reason why PR does not encourage voters of smaler parties to show their preference:
If your party under PR is polling near the treshold, most people will assume that it won’t make the treshold, and not wantig to waste their vote, chose another one.
(again an austrian example: in the 2008 parliament elections the liberal party contested again after a break, and was polling around 4-5 percent, in the days before the elction support slumped, and the pols sugested the aprty being near the 4% treshold, but appartently that unsetteled supporters, and the Lif got only 2,xx% at the ballot.

13. Costermonger Says:

Although AV has been lost, I am not despondent about voting reform in my lifetime (and I am much older than Prof Gowers). The reason for my degree of optimism is that the constitutional structure of the UK is under very considerable pressure. Devolution to Scotland has left the West Lothian Question unresolved. This is a sore point amongst many English people which eventually will have to be addressed. The SNP’s victory may not lead to direct independence for Scotland but it will force more attention onto the WLQ and it will be in Salmond’s interest to stir that pot. It is also worth remembering that the WLQ is a very potent issue for activist Tories. The most likely resolution to WLQ is a federal UK with an English Parliament with devolved powers, and a UK Parliament with responsibility for non-devolved matters: Foreign Affairs, Defence etc. When the English Parliament is established, how will its members be elected? Any such act of establishment will also require a wholesale review of the powers, functions, membership, and representation of a UK parliament. I would suggest that in both cases the form of election will be back on the table – and FPTP will no longer be a front runner.

14. Costermonger Says:

I have supported the negative income tax idea all my working life but recognise that the great difficulty is moving from the hotch potch system we have at present to a more logical and fairer system as represented by NIT. Whilst on the question of tax, and tax take, can I mention the Laffer Curve? Laffer noted that, at a tax rate of zero, take tax would be zero. He also postulated that, at a tax rate of 100% take tax would be zero (for a variety of reasons). Thus, somewhere between 0 and 100%, tax take will be maximised. This notion has been very influential with many politicians and commentators (not all on the right). Nobody knows what the shape of the function is, nor if there are multiple maxima, but empirical studies seem to show an optimum at 35% to 40%. Does anyone have greater insights than me?

• Richard Baron Says:

I have no greater insight, but I do know that it is incredibly difficult to get a precise answer. Controlled experiments are not on offer here. Even if you look at just one tax and the effect of changing rates, you still cannot tell. There has been a great deal of argument about whether the new 50 per cent income tax rate in the UK will raise extra money, and if so, how much. And we won’t even know after the event, because other things have changed in the interim.

We also have to define the question carefully. Do we mean the total tax take as a percentage of GDP, and if so, how is GDP to be defined (factor cost, market prices)? Or do we mean the marginal rate paid by most people of one tax, against a background of other taxes? And if we mean the former, do we envisage collecting the whole amount in a single tax, or splitting it among several taxes, which might well affect the behavioural effects. The choice of tax or taxes is especially important if you are an open economy that is a small proportion of the world economy, because capital is more mobile than labour.

Finally, do we want to maximise the tax take? Plenty of economists will argue that reasonably low-tax economies grow faster than reasonably high-tax economies, so that at any given time, the size of the state in absolute terms that will maximise present and future welfare is smaller than what would be the maximum sustainable size of the state in absolute terms at that time. (We have to relativise to a given time and switch to absolute terms to express this point, because the maximum size of the state in percentage terms is always 100 per cent, but then the absolute size of the state would be small because people would not work hard or efficiently.)

15. gowers Says:

Nick Clegg has chosen an interesting way to “fight back”: on this page is a transcript of an appearance of his on the Andrew Marr show in January. If you scroll to about two thirds of the way down, you find him defending the NHS reforms to which he is so bitterly opposed, even going so far as to claim that they were in the Liberal Democrat manifesto!

16. pedant Says:

You appear to have omitted “Haringey” from your list of ten places that voted “Yes”.

[Thanks — corrected now.]

17. Chris Says:

A pretty good reform that could get through without a referendum would be allowing multiple candidates from the same party, with the number of votes ranking (for example) the Tory candidates, but all of the votes counting, eventually, for the highest ranked Tory.

People seem to get hung up with two completely arbitrary things;
1. Proportionality among parties
2. Possibility of small parties “breaking through”

Proportionality is not desirable in itself; representativeness (< ?) is. To go after proportionality seems like assuming the smallest unit of representation is a representative, but it's not it's an idea. A system that selects right-wing LDs and Labs and gives the Tories a small majority could be just as *representative* of a right wing electorate as a big Tory majority.

It seems to be much more reasonable to try and get a system where the electorate can dictate more directly the MAKE-UP of the major parties and just accept that, that the big three are pretty much here to stay.

We don't need the Green Party bringing in representatives with Green ideas, we just need Lib, Lab, Con representatives who have those ideas.

18. Roxie Says:

I read your blog alot, and I also read The Platonist and Studyhacks.com. I’m 46 and have just started my first pre-requisite unit of university via distance education in the hope that I will be in a position to study mathematics as a distance student. Unfortunately for the next study period I won’t be able to continue due to lack of funds for books. Life’s a bit tough when one is a single working parentof another uni student.

But I am hungry for knowledge and I take much joy sitting and enveloping myself in solid study for hours – alas my day job dumbs down my mental state so that by the time I am home, have cooked and washed dishes, the effort to re-start my mental faculties is rather great.

To read your long posts and those long posts of the other blogs is the only way that I get through my day. I read them whilst I’m working a mundane job, and I manage to get through all of my work very very fast and accurately.

I for one, consider your work exemplary – and look forward to properly understanding the discipline in the future, and even though I don’t posses the required knowledge to understand your level of mathematics, my opinion of those who brush off your opinions because it is ‘too long’, is very low.

I work with adults like this, and most of my time conversing with them is also spent mentally trying to figure out ways to keep my discussions succinct because invariably, during conversation, I witness their eyes darting from my face to the walls, the floor and desks.

Roxie

As I argued before, nobody in the AV-YES camp had a coherent argument as to why AV would have made us materially better off. I asked many passionate supporters of AV why they thought it would make things better on the ground, and nobody said anything sensible.

Ultimately I think that AV played on the cognitive biases of the left – ideas that are pleasant to think (“more representative version of democracy ==> better outcomes”) but less easy to give empirical evidence for.

Nothing gained, nothing lost as far as I can see.

• gowers Says:

I’m not sure such an argument exists (in either direction). But it’s not the whole issue. For instance, I think most people would object to the idea of a dictatorship even if the dictator was a brilliant economist who could make us all better off.

One argument that has at least something to do with material well-being is that if the number of unsafe seats goes up, then the competing political parties have to appeal to a wider section of the country. At least in theory, if there are just a few marginal seats and if the people in those seats have characteristics in common (on average), then it makes sense for a party to tailor its policies in a way that advantages people with those characteristics. So switching to AV might have made people with those characteristics worse off and a broader set of people better off.

> most people would object to the idea of a dictatorship even if the dictator was a brilliant economist who could make us all better off

then would they not be fools? OR worse, would they not have turned democracy into a quasi-religion?

• gowers Says:

I think the best argument for democracy is that it gives you a safeguard if the regime turns nasty (unless, of course, it suspends democracy). If your only concern is your present-day material comfort, then in principle a really good and talented dictator could be better. But if you are interested in your future material comfort as well, and are not 100% certain of the permanent goodness and talent of your dictator, then it’s probably worth trading in some of your present-day material comfort for the security of being able to get rid of him/her.

I don’t know this for a fact because I haven’t spoken to enough people who live under dictatorships, but I would guess that the feeling of powerlessness you get from … er… having no power is a drain on the morale. I would also guess that in countries that obtained democracy at significant cost to living standards after 1989, very few inhabitants would have liked to turn the clock back (though in those cases the preceding dictatorships were hardly benign). I’m not sure what point Yankee is making below, but China is another interesting example. I think one could make a serious argument that in China an evolutionary change towards democracy would be better than a revolution. However, one could also make a serious argument that the pace of evolution so far has been much too slow …

• Richard Baron Says:

I agree entirely with Timothy Gowers on the benefits of democracy. We need to be able to throw a government out. I would add a few other points, as follows.

It is most unlikely that a talented dictator could organise the economy to produce better results than a mixed economy with a substantial (well over 50 per cent) free market element. The problem of what to make is just too complex to solve by anything other than the distributed processing of the price mechanism. Centrally planned economies have been disastrous, over and over again. There is no reason to think that modern mathematics and computational power would change that.

Suppose that we lived under an enlightened dictator, who granted us the freedoms that we now enjoy (speech, travel, etc). We would give up those freedoms ourselves, in that we would self-censor in order not to provoke the dictator into turning nasty. Compare Quentin Skinner, “A Third Concept of Liberty”, available in various places including Goodin and Pettit (eds.), Contemporary Political Philosophy, Blackwell, second edition, 2006.

Life under the Eastern European dictatorships was indeed hideous for any thinking individual. I have no direct experience, but have talked to enough friends who have. The point was beautifully, and chillingly, put by a friend from Romania, George Ross, recently deceased. He said there were five dont’s:

1. Don’t think.
2. If you think, don’t speak.
3. If you speak, don’t write.
4. If you write, don’t sign.
5. If you sign, don’t be surprised.

20. Yankee Says:

“I think most people would object to the idea of a dictatorship even if the dictator was a brilliant economist who could make us all better off.”

21. R. Moid Says:

I ended up voting “yes”, despite arguing against “yes” in comments on this blog, but not because of any of the arguments of the “yes” campaign. In the end, the misinformation and distortions of the “no” side annoyed more than the misinformation and distortions from the “yes” side, and I didn’t want AV to be defeated by too large a margin.

The main reason PR appealed to a lot of people in the past is that they believed there was a natural “progressive majority” and that the Tories were getting in because it was split between Labour and various versions of the Lib Dems. Maybe that’s even true. But the way the Lib Dems behaved after the last general election makes it seem more like a myth, especially in party terms. The Lib Dems now seem a lot like Tories by another name.

With the coalition saying they were going to stay for a full five years, and redraw constituency boundaries in the meantime, it looked like we might never be rid of them, and the AV vote was one of the few chances we’d have to get at them.

Then, where was the argument that AV would actually deliver any large difference that people wanted? Scotland uses a PR system and even uses STV is local elections, yet no one could point to any significant difference that made vs FPTP, and of course AV would seem even less likely to deliver.

22. Rapunzel Says:

http://bcakwords.blogspot.com/2011/04/why-i-am-voting.html

23. Antione Says:

Politics in general is crap game. I am low income but I don’t agree with all the moves the dems make. The republicans on the other hand had their fun for years and started this recession mess in the first place.

24. Gil Kalai Says:

I gave a course about the beauty of mathematics to humanity students and I mentioned both questions in combinatorics and about elections (they also had a vote on the AV/FPTP which end up 9:0 AV and 60 abstains (I did not vote))

In the exam I asked them in how many ways we can select a committee of 3 from 10 people. I was asked if these were correct answers:

A) quite a few, majority, dictatorship, approval voting AV, FPTP, …

B) there are precisely 4 ways!: with repetition where order matters; with repetitions with order does not matter, without repetition with order matters, without repetitions with order does not matter.

• Gil Kalai Says:

Still another aswer is: C) Truly a huge number. There are many many ways to chose the 10 people to start with and then quite a few ways to select the 3 from the 10.

• Richard Baron Says:

Gil, the fact that the students were so creative in finding ways to take the question that would make it easy to answer without the need for study of the facts that you had put in front of them during the course, shows that there were some budding politicians among them.

25. sisn Says:

Maybe you (or some of the other readers) find this lecture of Eric Maskin of the IAS in Princeton on
“Elections and Strategic Voting”
interesting.

26. מצברים Says:

מצברים…

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