Range Voting for Condorcetists

1. We argue that if the voters are all maximally honest, then range voting outperforms Condorcet voting methods.

The classic over-simplified and over-dramatized example is the "kill the Jews" vote where the choices are
  1. Kill the Jews and steal their money, using it to reduce taxes for non-Jews.
  2. The Jews (who are a minority) live.
  3. (Possibly other choices too.)
With honest Condorcet voting (by which I mean, honestly indicating the choice that is best solely for that voter, no matter how slightly), A wins.
But with honest range voting if the voters honestly express weak preference for A but strong preference for B (because the voters who benefit from reduced taxes wish to indicate honestly that is a small gain for them, while the Jews who die, wish honestly to indicate that is a large loss for them), B can win. B is better for society overall.
This example illustrates the fact that, if there is enough voter honesty, range can deliver superior results than any other of the usual voting method proposals. No other commonly-proposed voting method can avoid the "tyranny of the majority" problem. (Although this example was over-dramatized and over-simplified, scenarios like it do arise all the time, e.g. as of 2009 the "Swiss minaret ban" and various referendums on banning "gay marriage" might be abstractly comparable.) Bayesian Regret simulation data backs this all up by giving experimental proof Range yields superior results with honest voters.

2. On the other hand, if the voters strategize, then Range voting actually elects Condorcet winners more often than Condorcet methods. In other words, by exactly the yardstick Condorcet-supporters want, range voting is superior to Condorcet methods!

Q. How can this be? I thought the whole point of Condorcet voting methods was that they always elect a Condorcet winner (whenever one exists)?!?

A. Yes, but not if the voters are strategic (i.e. dishonest).

The model we shall examine is the following:

  1. We suppose honest voters elect candidate C who is (perhaps) a Condorcet winner.
  2. But that was just a pre-election poll, not the real election!
  3. Now in the real election, the voters are assumed to strategize. Those voters who are anti-C will therefore "bury" C because (clearly, as was just proven to them by the pre-election poll) honestly voting is not good enough strategically for their purposes. (Pro-C voters can try to counter by artificially raising C to top.) Consequently, in the real election it sometimes will happen that C will not be elected, even when C is the honest-votes Condorcet winner, and even if we employ a Condorcet vote-counting method. How often does this happen? That is what computer simulations can tell us.

We can also do the same computer experiment with both the pre-election polls and real election being held with some other voting system. We tried plurality, range, approval, and IRV. In the real election, we assume the voters exaggerate maximally on A and B – where A and B are the top-two finishers in the pre-election poll – as a strategic move to maximize the impact of their vote.

It can be proven that in this model, Approval and Range voters will always elect the Condorcet Winner (CW) [whenever a CW exists] if the CW was one of the top-two finishers in the pre-election poll (and also sometimes even if it was not). We can, by computer, determine how often these things happen.

The result of the simulation study is that range voting leads to a probability somewhere between 94% and 100% of electing a Condorcet winner in the real election (assuming 3-to-9 candidates run, and random election model, and restricting attention to elections in which a CW exists).

Plurality, IRV, and approval, however, all lead to substantially lesser CW-election probabilities: 64 to 96% depending on number-of-candidates (3 to 9) and election method, and always less than for range voting.

If you are a Condorcet fan, this range result ought to be highly satisfactory to you. Frankly it seems like if you get a result this close to your desires – 94% to 100% – you ought to quit whining!

But ok, you might not be completely satisfied and might still want to get that additional 0-6% of potentially-available Condorcet winners.

So therefore, you might say "let's use a Condorcet method!". However, the computer simulations show that, in this same model, all the Condorcet methods tried (and I tried a lot of them) actually yield substantially smaller chance of electing a Condorcet winner, than range voting.

Which leads you, as a Condorcet advocate, into difficulty. Why are you advocating a more complicated voting method that is less likely to lead to what you want (electing Condorcet winner)?

So then how are you going to escape from this quandary? Possible choices:

  1. Cover your eyes, say you have a headache, and refuse to accept or notice it.
  2. Say that voters will not actually be strategic. They will be honest. But in that case range voting is better than Condorcet voting as we already saw (#1 at top).
  3. Say that voters in the pre-election poll will not be honest, they will be strategic. But the simulations indicate that range, even with 50-50 mix of honest+strategic voters in the pre-election poll, still leads to higher probability of electing a CW, than does Condorcet even if Condorcet enjoys 100% honest voters in the pre-election poll.

    And even if in the pre-election poll the range voters are 100% strategic, i.e. they are approval voters – the same simulations indicate we get about 50% more Condorcet winners than Condorcet methods yield, even if the latter enjoy 100% voter honesty in the pre-election poll! (And this all in in a sim-scenario intentionally chosen to try to make range look bad!)
  4. Decide you should SUPPORT RANGE VOTING since it experimentally leads to more Condorcet winners and is simpler than Condorcet voting. The former means range is better by the very measure you, as a Condorcet advocate, claim most-matters. The latter means range is more-adoptable and hence more likely to actually happen.

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