Wednesday, August 30, 2006

Are Voters Rational? (3)

Although this section is part three of four, it makes up about half the essay. It deals with the central components of a Rational Choice explanation - the benefit, probability and cost - as well as one feature that seems problematic, duty.

III. Benefits, Costs and Probabilities

RCT predicts that people will vote if the expected benefits outweigh the costs, that is if Benefit x Probability > Cost. The benefit is the instrumental good of one’s chosen candidate winning the election – i.e. how much better they are than the next candidate – for now, I set aside ‘consumption benefits’. The probability is the likelihood that one’s vote actually makes a difference. For simplicity, I assume the cost is a given – the time and effort taken to vote, including perhaps time spent information-gathering, and I exclude, for example, the risk of being run over on the way to the polling station.

The reason it appears prima facie irrational to vote is that, even when B is very large, P will be so low amongst a large electorate that the expected benefit (B*P) will be near zero. As Green and Shapiro put it “Even if an individual would in principle trade $10,000 to determine unilaterally the outcome of a presidential election, the likelihood that she will cast the decisive vote in an actual election is vanishingly small. If we were to post odds of such an occurrence at one in a million, the expected value of the collective good in question is a penny”. Even if this underestimates P, and the chances were as high as 1 in 20,000, then the expected benefit is only equivalent to 50 cents. While someone might, for example, stoop to pick up half a dollar, they would be unlikely to walk to the end of the road even if they knew they could do so. Thus, it is puzzling why people should go to any more effort to vote. I will examine the three variables (B, P and C) in turn, and then briefly comment on a fourth – Duty – not so amenable to an RCT approach.

a) Benefit
The benefit of winning an election depends on the difference between one’s preferred candidate and the one who would otherwise win. Where two candidates are very close together, e.g. competing for the median voter, this is likely to be small. If one candidate is a relative extremist, e.g. Le Pen in France, then the benefit may be quite substantial.

It is often assumed the benefits that matter are those to the individual in question. As such, they might include lower taxes, welfare benefits, and state policies that happen to be tailored to the individual’s particular situation (e.g. suppose they are paying off a mortgage and have two children in the mid-teens, then a government that wants to lower interest rates and abolish university top-up fees would be in their interests). Feasibly, in this situation, the personal benefit could well be as high as $10,000, or even more. In reality, the difference between likely winners will probably be less, but even so an individual could have a lot to gain – or lose – from the result of an election.

Ordinarily, we would go to considerable effort to obtain a large benefit – for example, when contemplating large purchases, people often engage in much more market research and shop around for the best prices. RCT says what matters, however, is the expected benefit. While we’d do a lot for $7m, we wouldn’t do so much for a lottery ticket that had only a one in 14 million chance of winning this jackpot; it’s expected benefit is only 50 cents (assuming there are no other prizes). I will come to discuss probability next, but it is clear that the chances of one’s vote making the difference between success and failure are very low (as with winning the lottery), so even a benefit in the region of $10,000 is not enough.

Might the benefit be higher? So far, we have focused only on benefits to the individual, and perhaps the household to which s/he is so closely tied. We could, however, widen this interdependence. One might very well care for a wider group of friends and family. One will therefore want a government that not only best serves one’s own interests, but does good for everyone – e.g. by preserving law and order, and keeping the economy running smoothly. If so, there are far wider benefits to consider – not only you keeping your job, and being better off, but all your friends doing likewise. Most of us would, I think, go to some trouble to see our friends and family prosper. Indeed, if one feels some solidarity for one’s fellow citizens, then one may well want what is best for all of them – so if one genuinely believes the Democrats better than the Republicans, for instance, then one’s vote could mean a better government for 250 million people. Once we pass from egoism to altruism, we see the benefits may in fact be very large.

b) Probability
Whatever the relative merits of candidate X over candidate Y, however, if one of them will win regardless, then one’s own vote will achieve nothing to realise the potential benefit. If the benefit is high enough, one may take other measures to try to secure it – this is why rich businessmen make large donations to political parties, or use their media control to influence many other voters – but so long as one’s own vote makes no difference, the expected benefit of casting it is zero.

Calculating the probability of one’s vote making a difference, even to a quite inexact degree, is extremely difficult. For one’s vote to be pivotal, however, it means candidates must be separated by no more than one vote – so one’s vote can either turn defeat into a tie, or a tie into a victory. If there are only two other voters, two candidates, and each voter has a 50% chance of voting for either candidate, then the chance of one’s vote either way being decisive is 50% (this is just the probability that the other two will tie). As soon as we introduce thousands of other voters, a few more candidates, and crucially relax the assumption about how others are likely to vote, this calculation becomes almost impossible. We can see, however, by looking at our records that very few national elections are tied, or decided by a single vote.

One possibility is that people overestimate the value of P, and think they have a non-negligible chance of making a difference to the outcome of an election. If someone thinks he has a 1% chance of making a difference then this, multiplied by a potential benefit of $10,000, means he expects a benefit of $100 from voting. In this case, it would seem quite rational for him to vote – though we might question the rationality of the belief that leads him to this conclusion.

People are notoriously bad at judging small probabilities – a fact that perhaps accounts for buying lottery tickets. The fact that unlikely events receive more attention in the media than the everyday increases their salience, and makes them seem more likely than they are. Moreover, most people reportedly have an inflated sense of their own importance and ability to influence events. Perhaps this contributes to the fact that people prefer to travel by car rather than plane even though the latter is statistically safer – being in their own hands provides an ‘illusion of control’, and most people believe they are better than average drivers, and so less likely to have accidents. In some situations, these traits may be adaptive – some have suggested those with a true assessment of their self-worth are the depressed – but they don’t conduce to rational decision making when small probabilities are concerned. Many people may well over-estimate the probability of their being able to influence events, and Blais finds evidence this is indeed the case for a significant number of voters. Their decision to vote may be rational, given false (and perhaps admittedly irrational) beliefs they hold about its efficacy.

So long as benefits remain finite, a low probability keeps expected benefits low, and thus seems to make voting irrational. Is there any way P might be higher? Firstly, it is worth noting that the fewer people vote, the more chance one has to make a difference. If everyone were to abstain, then a single vote would then be enough to determine the outcome of the election, realising B, and so be rational. If RCT advises us not to vote in normal circumstances, then this is self-limiting, for when turnout drops low enough it becomes rational to vote.

P will also be higher in close-run elections. If one knows that 80% of the electorate are disposed to vote for a given candidate (X) then, unless turnout is much higher amongst non-X voters, the outcome is foregone. Whether or not one is in favour of X, one’s vote won’t make a difference either way. If the election is much closer, however, then one’s vote seems to matter more. While it is still unlikely that the election will be decided by a single vote, there is a greater chance that one’s vote will be decisive, so it is more rational to vote in close elections.

These facts merely repeat the observation that P varies between contexts. What is needed to make voting more rational, however, is a much higher value of P. One obvious way in which P could be higher is if one had more votes, but this is not the case in any democracy. It might be that one effectively has more votes, however, if one is a prominent community leader, and knows that many others will follow one’s example and vote, though they may not otherwise. (This may be why leading political figures like to vote early and with media coverage).

There is a danger that people will still be over-estimating P, if only by over-estimating their impact on other people (but also because, even if one effectively brought 50 votes, that would rarely decide a result). Blais points out that people may be guilty of confusing diagnosis and cause: they begin by reasoning that if everyone who reasoned as they did voted it might make a difference, and then vote as if they alone were responsible for all of that higher turnout. It would obviously be irrational for the ordinary voter to act as if his/her decision to vote also made the difference as to whether many others voted. People needn’t, however, be making the mistake Blais accuses them of – they may, for example, be employing Kant’s universalisability test: since they couldn’t will that everyone abstain, they hold themselves morally obligated to vote.

Whatever people’s actual reasoning, it is clear that, in a large electorate, P is low, and so even if B is substantial any expected benefit (B*P) must be relatively small. A small expected benefit is still worth having, the question we must now turn to, however, is its cost.

c) Cost
If one could acquire a small expected benefit – whether a certainty of a small benefit (say, 50 cents), or a small chance of a large one (say, a 1 in 2,000 chance of $1,000) – by something as simple as scratching one’s nose then, in the absence of any other compelling reason to act differently, it would seem that one ought rationally to scratch one’s nose (especially if, for example, one already wanted to scratch one’s nose for an itch). One would be unlikely, however, to go to much trouble – say a 50 minute round trip – for the sake of such a trivial benefit. If voting is a similarly small expected benefit, then its rationality all comes down to the cost.

The act of voting usually involves a relatively short journey to a polling place and, once there, giving one’s name or number and marking a cross on a piece of paper. For most people, this is likely to take around half an hour (of course, some will be lucky enough to live very near the polls, but others much further away). What is the opportunity cost of this time? We earlier suggested the expected benefit to be less than a dollar; so, assuming an hourly wage rate of just $5 – a rather minimal wage – and a time loss of just 15 minutes (below average), it still seems the ‘cost’ of voting ($1.25 in monetary terms) is greater than the expected benefit.

But is the cost really so high? Many people questioned reported that they had little better to do. I think it’s true that many people on most days have some ‘dead time’ when they don’t do much very productive. Perhaps the time is spent resting, watching TV (even just channel surfing), or on minor household chores that could have been put off. To take half an hour out of this time to vote isn’t much of a loss. Further, since elections come round but once every four years, while many of these other activities can be indefinitely postponed, probably no less worthwhile than any alternative. Moreover, many people enjoy a walk occasionally, if only for exercise or to pick up the daily newspaper. It’s far from clear that the ‘cost’ in going to vote is much of a cost at all.

Those who think costs are too high might protest that the cost is not just a trip to the polls, but includes deciding who to vote for. For a start, there are considerable costs of information gathering – following current affairs and studying party manifestoes. Once such data has been collected, one still needs to make an all-things-considered judgement who is best to vote for. Especially if parties are close on many issues, and given that the issues involved in running a modern country are often very complicated, it might take people a considerable cognitive effort to decide, on the basis of evidence, who to vote for.

Again, however, these costs may be exaggerated. Many people follow the news anyway – even if not reading daily newspapers, they pick up major stories from word of mouth, or even satirical current affairs shows like Have I Got News For You. A working knowledge of politics, sufficient to inform a vote, is little effort – for many people, it is simply a part of their general knowledge. While they may not be experts on political affairs, they know enough – given that they do not single-handedly determine the outcome, it is not rational for them to be better informed. Their low impact (P) actually reduces the costs of the decision, since casting a relatively uninformed vote need not be disastrous. As for those who still have difficulty making up their mind, it seems for them B is very low, so it may be quite rational for them to abstain. For those who perceive more at stake, it will usually be quite obvious who to vote for.

It seems that, for many people, while B*P is very low, C is also very low. Given that the costs and benefits are so small, and there is little ‘punishment’ for irrationality, it seems unsurprising that RCT is not a particularly powerful predictor. Indeed, some have gone so far as to suggest (given the costs of calculation), that it would be irrational to explicitly calculate costs and benefits – thus a ‘satisficing’ approach, that results in either voting or not voting but without much deliberation as to whether to, is actually maximal.

d) Duty
The B identified above was an instrumental one. There may also be an intrinsic benefit, however. Some analysts include this under a sense of duty, but it is not entirely clear that this is correct – duty need not benefit one (one may regard visiting an elderly relative as something of a burden, but do it anyway), this is distinct from finding an activity intrinsically worthwhile. One may value voting because it recognises one as a competent decision-maker, provides one with an ‘illusion of control’ and differentiates one as an active citizen rather than passive subject. Alternatively, one may indeed regard voting as only instrumentally beneficial, and all together a net cost, but see it as an obligation – perhaps a duty not to free-ride on other citizens out of fairness, or a feeling one should use one’s vote out of respect for the fact it was hard-won (such sentiments are likely to be stronger amongst the more recently enfranchised, e.g. blacks and women). While turnout is traditionally low amongst the younger voters, an 18 year old may vote simply because they have reached an age where they can – it is a novelty, or coming-of-age ritual. None of these motivations are included in the standard RCT analysis, which considers only instrumental benefits for fear of (even more) vague, unobservable or unfalsifiable predictions. Nonetheless, none of these considerations would seem to mark voters as irrational, as I hope to show in the next section.


At 11:28 am, Anonymous Paul Davies said...

Good stuff Ben. There're another couple of points which I think are relevant.

A lot of RCT stuff is rather myopic and looks only at events on polling day. Yet there is a whole 'hope' factor thing, as people tend to expect too much of a new government, and thus their expected benefits are not so much about influencing the result, but about how such an influenced result will result in living in some sort of Eden for the next few years.

Related to this, in a way, is how reponsive the govt, once elected, is to the wishes of the people. In places like the US, for example, the constitutional set-up is a lot less responsive to elections than, say, Malta, which has a predictable affect on expected benefits.

(slightly more discussion on this, and a link to a tedious paper on it via my name link)


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