It was conjectured by Range-doubters that range, while it works well with 100% honest voters, and also well with 100% strategic voters, might not work so well with a mixture of the two. The problem would be if (say) more Bush than Gore voters were strategic, leading to a huge advantage for Bush.
In the computer simulation experiments below we employed a 50-50 honest-strategic voter mix (a composition that seems approximately realistic based on our polling studies) in which each voter chose whether to be honest or strategic by flipping a coin. Note: it then is entirely possible in each election for Bush (or Gore) to get more strategic voters, and since the number of voters in each election below was only 61 (not huge) such an imbalance was in fact highly probable and typical and must have hurtfully impacted range's Bayesian regret numbers.
As Kevin Venzke put it:
If I don't want to assume that voters will courteously vote sincerely (even when this limits their power to affect the results), then I wouldn't use Range, as the result will be rather randomly skewed based on who chose to exaggerate and who didn't.
So – what happens? Answer: despite these circumstances, Range still kicks the butt of all the other ≈50 voting methods available in our computer sim package IEVS 2.53, getting the lowest Bayesian regret scores. In particular, Range is superior to Approval voting (in which all voters are "forced" by the rules to be strategic, even if they want to be honest), i.e. what Venzke called "random skewing" actually helped, not hurt.
Here is a typical run trying 29999 elections:
|Voting Method||Regret||#Agreements with (true-utility-based) Condorcet Winner (when CW exists)|
and now, just to make things ultra-clear, let's do a run with 13-voter elections
just to make range really suffer heavily from this effect:
|Voting Method||Regret (50-50)||Regret (100% honest)||#Agreements with (true-utility-based)
Condorcet Winner (when CW exists)
So... the range-doubters look to be just wrong.
Note that Range Voting is at the top of the heap (lowest Bayesian regret) in both these tables, except for
Also note that Range and its variants (Range2Runoff, Approval2Runoff) in these simulations with 50% honest voters actually yield the true-utility-based Condorcet winner more often than any other method, including "Condorcet methods" shown colored. That counterintuitive conclusion was forecast in a different model of strategic voting than the one simulated here. (The one here involves voters who believe a priori that candidate k+1 is far less likely to win than candidate k, and act accordingly to maximize their vote's impact.) This is a very strong reason not to prefer Condorcet voting methods over range – with a 50-50 mix of strategic and honest voters, range actually does their own job better than they do!
Caveats: IEVS 2.53 is still an early version and does not contain a lot of voter strategies and utility generators planned for later IEVS versions and which had been in my old (1999-2000) simulator. In particular, all rank-order voting methods shown here are strict rank-order, i.e. with rank-equalities forbidden in ballots. It has been suggested that variant-methods in which rank-equalities are permitted – especially Condorcet methods based on the "winning votes" concept – would handle strategic voters better. That is probably true. If wv-condorcet strategy were the same as approval-voting (and it definitely is not, but that might be a semi-decent approximate view) then in fact range and wv-Condorcet methods would all exhibit identical Bayesian Regrets with 100% strategic voters, and presumably considerably closer-than-here-shown BRs for a 50-50 mix, although I would expect Range still would have better (i.e. smaller) BRs. Also, in that case, range might no longer be better than Condorcet methods for the purpose of generating honest-voter Condorcet winners in the presence of strategic voters. All this, however, has to be regarded as speculation until more advanced IEVS versions appear that are capable of handling equalities in rank-order votes.
This objection was raised by one of our critics. We respond
Two possible ways to look at it:
Another set of computer sims
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