# Maximum entropy methods for single-winner elections?

Dear Lazyweb,

You’ll never believe what happened to me the other… err. Sorry, wrong post.

So I read this paper the other day: http://www.votingmatters.org.uk/ISSUE26/I26P3.pdf

It’s a good idea. Essentially the idea is you apply the maximum entropy principle to probabilistic voting systems: You take the distribution on Perm(Candidates) which maximises entropy subject to the constraints P(x < y) = fraction of the voters who think x < y. This is satisfiable because random dictator has these constraints. The biggest problem with it is that it requires you to do a linear optimisation problem in N! - 1 dimensions, which isn't great. Additionally, I'm mainly interested in randomized methods for single-winner elections, which have a much smaller number of dimensions. I was wondering if there was a natural analogue to the idea for this case. Can anyone think of one? Obviously you can consider the maximum entropy distribution on Candidates, but it's not obvious what the equivalent constraints should be. Thoughts?

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## 2 thoughts on “Maximum entropy methods for single-winner elections?”

1. Veky

WTF?
You might say that here in Croatia we have kind of such a system. Every government spends more than half of its mandate trying to reverse the measures taken by the previous one, because they are “obviously bad”. And people vote for “anything but those currently in power, noone else is that incompetent”. As a consequence, we are at a standstill for about 20 years.

The continuity of government is very important. I might say it’s the main reason for representative democracy itself. You don’t achieve anything by randomly changing the direction country is headed to.

1. david Post author

It’s worth noting that in this context “single winner elections” doesn’t necessarily mean “the ruling party”. It may also mean “On this particular issue” or “For this particular member of our parliamentary body”.

Paradoxically, introducing randomness into a procedure can actually improve its long term stability if you’re running it many times: The problem with deterministic voting procedures is that they’re very susceptible to small changes in the status quo because you’ve forced an unnatural discretization. You see this every election in somewhere like the UK or US where tiny changes in the popular vote can produce landslide victories or defeats. By introducing randomness to that process you can produce something with much more consistent results.