What your vote is worth - a back of the envelope calculation

[diziet]

tl;dr: Your vote really counts!

Each vote in a UK General Election is worth maybe £100,000 - to you and all your fellow citizens taken together. If you really care about the welfare of everyone affected by actions of the UK government, then it’s worth that to you too.

• Introduction
• A method for back of the envelope calculation
• UK Parliament
• European Parliament
• Only if you care about other people as much as yourself!
• This is a very rough analysis
• Conclusion

Introduction

It seems a common perception that one vote, in amongst all those millions, doesn’t really matter. So maybe it’s not worth voting. But, voting is (largely) what determines what the government does - and the government is big. It’s as big as all the people.

If you are the kind of person who cares about what happens to everyone in your polity and indeed everyone its actions affect, then even your one vote is very important indeed.

A method for back of the envelope calculation

It would be nice to give a quantitative estimate. Many things in our society are measured in money, so let’s try taking a stab at calculating the money value of your vote.

The argument I’m going to make is this: the government (by which I include the legislature), which is selected by our votes, decides how to spend the national budget.

So, basically, I’m going to divide the budget, by the electorate.

UK Parliament

UK Parliamentary elections decide not only the House of Commons, but, through that, the government. The upper house, the House of Lords, has very limited influence. So I think it’s fair to regard the Parliamentary election as, simply, controlling that budget.

Being lazy, I’m going to use Wikipedia data. We have the size of the electorate, for 2019, 47.6 million. But your influence isn’t shared with the whole electorate, only with the other people who also vote. Turnout in 2019 was 67.3%. The 2019 budget isn’t listed but I’ll just average the 2018 and March 2020 figures £842bn and £873bn, so £857 billion. (Strictly speaking I should add up the budgets for the period of the Parliament, but that seems like a lot of effort.)

There’s a discrepancy in the timescale we need to account for. Your vote influences the budgets for several years, depending how long it is until the next election. Taking Wikipedia’s list of elections this century there’ve been 7 in 24 years. So that’s an average of about 3.4y.

So, multiplying it through, we have (£857b * (24 / 7)) / (47.6M * 67.3%), giving a guess at the value of your UK General Election vote:

£92,000.

European Parliament

2022 budget for the European Union (Wikipedia again) was €170.6 bn.

The last election, in 2019, had a turnout of 198,352,638. Each EU Parliament lasts 5 years.

The Parliament, however, shares responsibility for the budget with the European Council, which is controlled, ultimately, by national governments. We have to pick a numerical value for the Parliament’s share of the influence. Over the past years the Parliament has gradually been more willing to exercise its powers in this area. I’m going to arbitrarily call its share 50%.

The calculation, then, is €170.6 bn * 5 * 50% / 198M, giving a guess at the value of your EU Parliamentary Election vote:

€2150.

This much smaller figure reflects simply that the EU doesn’t spend very much money, for a polity of its size. (Those stories in the British press giving the impression that the EU is massively wasteful are, simply, lies.)

The interaction of this calculation with the Council’s share of the influence, and with national budgets, is a bit of a question, but given the much smaller amounts involved, it doesn’t seem worth thinking about that too hard.

Only if you care about other people as much as yourself!

All of this is only true for you if you value and want to help everyone in your society. That includes immigrants, women, unemployed people, disabled people, people who are much poorer or richer than you, etc.

If you think about it in purely personal terms, your vote is hardly worth anything - because while the effect of your vote, overall, is very large, that effect is shared by everyone in your polity. So if you only care about yourself, voting is a total waste of time. The more selfish and xenophobic and racist and so on you are - caring only about people like yourself - the less your vote is worth.

This is why voting is rightly seen as a civic duty. I just spent £30 to courier my EP vote to Den Haag. That only makes sense because I’m very willing to spend that £30 to try to improve the spending of the €2000 or so that’s my share of the EU budget.

This is a very rough analysis

These calculations neglect a lot of very important things: politics isn’t just about the allocation of resources. It’s also about values, and bad politics can seriously harm people.

Arguably many of those effects of your vote, are much more important than just how the budget is set and spent.

It would be interesting to see an attempt at a similar analysis but for taking into account life and death questions like hate crime, traffic violence, healthcare, refugees’ welfare, and so on. I’m not sure how to approach that. Maybe some real social scientists have done so? References welcome.

Also, even on its own terms, this analysis is very rough and ready. We haven’t modelled the ability of the government to change its tax rates; perhaps we should be multiplying GDP (or some other better measure) by 90% percentile total tax rate amongst “countries like this one”. The amount of influence that can be wielded by one vote is probably nonlinear in the size of the political faction, but IDK in which direction. In unfair voting systems like the UK’s, some people’s votes are worth much more than others. In a very marginal constituency, which is a target seat, your vote might be worth tens of millions. In a safe seat, it might “only” be worth a few thousand. And in practical terms you don’t get to choose precisely the policies you want; you have to pick a party, which is sometimes very much a question of the lesser evil.

So, there is much I haven’t modelled. But the key point stands:

Conclusion

Although your vote is diluted by everyone else’s votes, together, we control the government, which affects us all. So if you care about the whole of society, the big numbers in the divisor, and the numerator, cancel out.

You can think of your vote as controlling one citizen’s worth of government activity.

edited 2024-06-01 09:40 Z to fix a grammar botch

Comments

[vyvyanx]

I like this analysis, for all its simplifications. But I think I would add that each person's vote is valuable not only for its impact on all the people in their society, but also for its impact on people in other societies (through governmental decisions on international aid, trade, migration...), other living things in the UK (via decisions on farming, fishing, land use, animal welfare...) and indeed the global biosphere both now and into the future (through decisions impacting greenhouse gas emissions, international trade...).

[diziet]

You're quite right, of course.

(Some of that impact is mediated through things the UK government spends money on - for example, the armed forces - so is captured by this money-based analysis. But much of it isn't.)

[lovingboth]

What I would say this misses out is that all votes in UK General Elections are very, very much not equal.

I have voted in.. let's see.. 1983, 87, 92, 97, 2001, 05, 10, 15, 17, 19.. ten of them. Plus a by-election.

In precisely one of those did my vote have any chance whatsoever of electing someone who I did not loathe, and it turned out that what would have been my second choice in '97 won.

I am optimistic that a tactical vote this time may get rid of the shit, but I may as well not bothered voting in any of them.

See also: US presidential elections.

[simont]

An unspoken assumption in this whole piece is the idea that probabilistic expectation is the right way to evaluate cost-benefit decisions, even in the kind of edge case where there's a very small chance of a very large change.

I think that one psychological factor that motivates voter apathy is the idea that your vote "doesn't make a difference" not in the sense that votes in general don't make a difference, but in the sense that with very high probability, your vote doesn't change who gets elected: almost certainly the election would have had the identical outcome in the alternate universe where you personally voted differently, or not at all, but everybody else voted the same as before.

Probabilistic expectation aligns with how things come out if the experiment is repeated enough times and the results aggregated. That's why it makes sense for insurance companies to offer the deals they do. But in a one-off case, where you won't have the opportunity to aggregate many results, if the outcomes include a tiny chance of a huge difference then an individual's decision can quite rationally go the other way – which is why sometimes it still makes sense for the customer to buy insurance. Or it can seem to go the other way, which is why people do fun activities with a tiny chance of a big disaster.

An election is aggregating in a different way. You don't get to add up the effect of your vote over even 20 general elections, let alone 10⁹, which might be just about enough that the chance of your vote swinging the whole thing might come up enough times to have an effect on the aggregate outcome. But it's aggregating in space rather than time: your vote is combined with many other votes in this election.

And I wonder if part of the issue is that the <20 elections in your lifetime are psychologically more salient than the millions of other people voting with you, so that it still feels like one of those one-off cases where the tiny chance of a huge difference gets neglected, rather than one of the nice linear cases where you (should) take it seriously, weigh up the smallness of the chance against the bigness of the change, and go with probabilistic expectation.