The Economics of Proxy Votes

A recent news report on the viability of  “proxy votes” got me thinking about the the mechanisms of elections. My skepticism is grounded in economic analysis, and this post sums up my concerns. 

Historically across democracies, elections (rigged or not) are rarely won by virtue of one vote. Taken individually, the marginal vote of any voter has little impact on the outcome. Victories in elections are thus decided in terms of what I’d call a “total relativity,” “total” because the votes garnered by candidates are aggregated, but “relative” because the aggregate are compared amongst candidates and the one with the highest aggregate relative to others is declared the winner.

What this means is that an election is essentially a zero sum game. An additional gain of one vote for a candidate means that the other candidates have lost one vote in relative terms. So to an individual voter their marginal votes have little influence on the outcome, but the converse holds for candidates I.E. a marginal vote will be more significant to a candidate than to a voter. That this is exacerbated when an election is close is self-evident as candidates joust for swing voters.

The way I see it it seems to be the rule of the world that democratic governance means the representation of those who both voted and had their votes prevail. What about those who chose not to exercise their civil right to vote? It probably meant they had little stakes on the political issues characterising a particular election. The apolitical nature of those who could not be bothered to vote – while worrisome to the civic-minded – has no impact on an election. Consider:

Suppose that of all eligible voters, there is a fraction of them, k, that couldn’t be bothered to exercise their votes. To all candidates in a district then the votes to fight for in order to win an election is now (1-k) multiplied by the number of eligible voters. Assume that there are only 2 candidates competing, and candidate A got a percent of votes while B got b percent of votes. If a(1-k)>b(1-k), A wins and if a(1-k)<b(1-k), B wins. So no matter what k is, so long as one candidate does better than the other in relative terms, there is no effect on the election. Our democratic principle is thus empowered by the will of the majority when voters chose either one of A or B. Whether or not there are a lot of people who chose not to vote does not concern us if we are chiefly concerned with the outcome.

Now suppose we introduce a “proxy vote” system and now the k fraction of voters who could not be bothered to vote are allowed by law to “transfer” their votes to some other voters. So that means that campaign managers will now have an incentive to “capture” the “k” votes out there and have it transferred to voters who are certain to vote for the candidates they campaign for. This leads to one of  of the following outcomes:

1)If the number of votes garnered by candidates A and B are equal, that is a=b, then the outcome is contingent upon who is more able to capture the “k” out there.
2) If a is slightly greater then b or vice versa, then again the outcome is contingent upon who is more able to capture the “k” out there.
3) If the election is a landslide election with a sufficiently greater than b, then it doesn’t matter who captures the “k” proxy votes out there if k is not a sufficient force to overcome the preference of the majority.

Scenario 3 does not bother us politically because it does not compromise the central tenet of democracy that is the prevail of the will of the majority. The economics of 3 however is very “inefficient” if capturing “k” votes has become such a norm that campaign managers incur a lot of cost to obtain them. Such efforts that promote no change in outcome are considered “wasteful” as they divert resources away and offer no gains. Just like the arms race, both A and B would still have had their relative positions maintained with or without incuring the extra costs to capture those “k” votes, and the fact that they both incurred those costs and had no change in their relative position thus made both worst off.

Scenario 1 and 2 do bother us politically and in an indirect manner, economically. Politically it means that democracy is redefined to be representation to he/she who is both most able to put additional weight to their votes and prevail. Is it still democracy when the majority prevails not because they have the people behind their numbers, but because they can make their votes count by “manipulating” the weightage of their votes? Economically, an election is valuable so long as it achieves its desired goal – which is to defend the tenet of democracy especially in safeguarding the will of the majority. If a “public good” such an election can no longer deliver its benefits, and now comes with an additional cost of wasteful campaign costs, to what degree is public welfare served?

This sounds distasteful if you are civic-minded. I understand that the “proxy vote” consideration comes from the intent to promote civic participation in democratic governance. If a proxy vote system makes no change in outcome as in 3), then why introduce it with the burden of the costs I have mentioned? If a proxy vote does change the outcome of an election at the expense of compromising our democratic principle, the question is – is such “civic proxy voting” ever going to justify the bastardisation of democratic voting?

PS: I have made the argument that proxy voting is a “transaction” between those who could not be bothered to vote to those who are committed to vote for a candidate. In reality of course a proxy vote might be desirable due to geographical,social or even personal constraints. However, that doesn’t mean that the model I have described here is completely inaccurate, this post is of course a simplified abstraction of reality.My argument is that if preference are more or less stable from the onset, converting indifferent votes to impactful marginal votes is costly regardless of how it affects the outcome of an election. I have implicitly made the argument that apolitical eligible voters are rather selfish in the sense that they’d “sell” their votes away with the “rational actors assumption.” This is meant to apply probabilistically across a population and there is no reason to assume that people who couldn’t be bothered to be vote would suddenly be bothered about the consequences of transfering their votes to people with vested interests.

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