# Overcoming the paradox of voting

This past Saturday the nation has elected its parliamentary representatives to create law for the Commonwealth of Australia. Who sits in the 150 seats of the House of Representatives and the 76 seats of the Senate is undoubtedly a question of national importance. One would think that the conclusion “I should vote” follows from this proposition, but does it?

Anthony Downs in his 1957 political science treatise An Economic Theory of Democracy first observed what is known in economics and political science as the paradox of voting. Simply put, the paradox is that many people decide to vote when the costs of voting almost always outweigh the expected benefits of voting. This is best demonstrated with a voter utility model, which states you should not vote if:

C > p(ALP – LNP)

Where C=the costs of voting, p=the probability that your vote will actually matter, ALP= the value you assign to the ALP forming government and LNP=the value you assign to the LNP forming government. If you prefer the LNP, you would just swap these two terms.

At first glance you may think voting doesn’t cost you anything. Whilst it is true that you don’t have to pay a direct monetary sum in order to vote it is something that involves time that could be spent on work or leisure. Furthermore, if you want to vote in an informed way and research which party’s policies are better for you then this requires a further investment of time which enlarges the cost of voting.

As for the right-hand side of the formula, it does not matter what values you assign to the terms within the brackets because the probability that your vote will actually matter is practically negligible. Even in one of Australia’s closest marginal seats, Corangamite, the margin of victory was still 771 in 2010. If the margin of victory is above 1 then your vote doesn’t matter. The probability of the margin of victory being low enough for your vote to matter is approaching 0. Therefore, as there are positive costs to voting the utility model will almost always state that a rational self-interested individual should not vote.

The common response to this is that “but if everyone thought like that then nobody would vote.” This is true, but the fact is that virtually nobody besides economists and political scientists think like this. Why does nobody think like this and why do so many people vote? Does this expose a shortcoming in the rationality assumption?

To explain away the paradox political scientists William H Riker and Peter C. Ordeshook added another variable to the Downs model. They believed the reason as to why people vote is that they feel a civic duty to vote. This can be modelled:

C > p(ALP – LNP) + D

Where D=civic duty and all the other terms are as aforementioned.

By voting people feel that they are playing their role in the democratic process, a process larger and more important than any individual. They derive some benefit from fulfilling this duty and they therefore vote.

However, we know from the data that duty and goodwill alone will not drive voter turnout. As fellow ESSA contributor Christopher Weinberg pointed out in a Melbourne Globalist piece, voter-turnout in the United States (which has a non-compulsory voting system) was 70.33% of registered voters, equating to only 53.57% of the voting-age population.  This can be contrasted to Australia (which has a compulsory voting system) where voter turnout in 2010 was 93.21%.

In Australia, a failure to vote without a valid reason is penalised by, at least, a \$20 fine. We can once again add this into the utility model:

C > p(ALP – LNP) + D + 20

With this utility model you can see it will now probably be the rational choice to vote for most people in Australia. This is because, although they will be unlikely to affect the outcome of the election, they will gain some intrinsic benefit from fulfilling their civic duty and avoid a fine. This employs the powerful force of what behavioural economists term loss aversion.

As Weinberg pointed out compulsory voting maximises voter engagement and pulls our politics to the centre. This is because rather than pandering to energised fringe groups the major parties are incentivised to appeal to the median voter. Although this is somewhat complicated by our electoral system, compulsory voting by and large makes for more centrist politics.

Most people find this rational choice model analysis of voting disturbing. This is because voting is an expression of a fundamental democratic right. It is an idea for which many have lost their lives and a right that so many people across the world are still deprived of. Rational or irrational, voting and democracy is a thrilling, crucial and glorious system, one for which we should all be thankful.