Simulating Voting Strategies

Jack Waugh

I want to simulate Score and IRV. A strategy simulation algorithm for either of these systems would take as inputs the sentiments of the voters toward the candidates and produce the vote that a particular voter would cast. In the real world, the strategy runs in the voter's brain and its inputs are the voter's sentiments and the voter's estimates of the sentiments of the other voters. But for simulation purposes, I suppose it is good enough to assume the estimate is completely accurate and drive the algorithm from the modeled sentiments of the simulated voters.

Of course, two obvious and trivial strategies are the "honest" ones for IRV and Score. But I would like better.

Who is able and willing to lay out an algorithm for one or more strategies that could serve their users better than the "honest" ones, to simulate for IRV and/or Score?

Keith Edmonds

@Jameson-Quinn did something like this for his VSE simulations.

rob

This is something I did a couple years ago that attempts to simulate strategy:
Youtube Video

The idea is that it initially runs a "naive" vote, where they simply vote in the most direct way without consideration of how others may vote. Then, in a number of rounds, they alter their vote based on how others voted... which basically eliminates candidates so they direct their votes toward those that are left rather than wasting their votes on those that are least likely to win. This simulates their ability to predict how others will vote. Note that some voters are more strategic than others (they range from orange to blue, orange being maximally strategic).

I haven't done score or IRV, but they'd be easy to add. I did add some additional features shown here, but apparently there is no audio on this one.
Youtube Video

I was kinda proud of the dynamic sorting animation, which I think allows your eyes to follow what is happening pretty well.

Jack Waugh

What is an example circumstance where a voter who is a toady for the plutocracy would reverse candidates on an IRV ballot?

rob

Jack I'm not sure what you mean by "toady for the plutocracy." Or maybe I should say, why is that relevant? I usually approach this generically, e.g. "A voter who has agenda X."

What do you mean by "reverse candidates"? Do you mean change their ordering from their sincere preferences? Say a voter prefers candidates in this order: A>B>C>D>E. However, all indications (based on polls, based on the voter's intuition, or whatever) are that B and E will be the front runners. In that case, the voter might want to vote B>A>C>D>E, to give B the best chance of beating E.

tec

Warren D. Smith's Range Voting paper (2000) and his C code simulation goes over a number of different voting systems and simulates both honest and "rational" ballots for many of the voting systems he covers. The 30 voting system and strategy permutations in the paper are: (In the paper, WDS starts his list with zero and the "as 25" strategy reference is "as 26")

Honest range voting (scaled utility vote)
Honest Borda
Honest Condorcet Least-Reversal (CLR)
Honest Coombs STV (most least-liked candid eliminated each round)
Honest Hare Single Transferable Vote STV (least most-liked canddt eliminated)
Honest Copeland (win most pairwise elections)
Honest Dabagh point-and-a-half
Honest Black (if no Condorcet winner use Borda)
Honest Bucklin
Honest plurality+runoff for 2 top finishers
Honest plurality (1 vote for max-util canddt)
Honest bullet (1 vote against min-util cand)
Majority vote on random candidate pair
Random "dictator" voter dictates winner
Random winner
Worst-summed-utility winner
Honest approval (threshhold=avg canddt utility)
Strategic range/approval (average of 2 frontrunner utils as thresh)
Rational range/approval (threshhold=moving avg)
Rational plurality (vote for 1 of 2 frontrnnrs)
Strategic Borda I (1 frontrunner top, 1 bottom, rest recursively)
Rational bullet (vote against 1 of 2 frontrnnrs)
Strategic CLR (strat same as 25)
Strategic Hare STV (strat same as 25)
Rational Borda (1 frontrunner max, 1 min, rest using moving avg to decide if max or min vote)
Strategic Coombs STV (strat same as 25)
Strategic Borda II (1 frontrunner max, 1 min vote, rest honest)
Rational Dabagh point-and-a-half (moving avg)
Strategic Copeland (strat same as 25)
Strategic Black (same strat as 25)

(A Google search for rangevote.pdf will get you to the paper. His c code is at: https://www.rangevoting.org/WarrenSmithPages/homepage/votetest2.c)

I hope this provides some good options for your strategy simulations.

--tec

Jack Waugh

What if the voter favors both front runners and opposes everyone else? Will that voter have an incentive to vote other than "honestly" in IRV?

tec

That question gets right to the heart of the problems in IRV. A paper by Bartholdi and Orlin (1991), Single Transferable Vote Resists Strategic Voting, suggests IRV should be used because it is so difficult to figure out how to vote strategically. The question a rational voter faces when filling out their IRV ballot involves both the accuracy of the polling data, and what the polling data shows. If polling shows both front runners are significantly ahead of an unacceptable third choice and the sum of the top three poll numbers is significantly larger than the sum of the poll data for the remaining choices, then an honest IRV ballot is probably a strategic ballot. But the devil is in the details, or more specifically the eliminations. Here's a scenario that might answer your question.

Suppose there are five alternatives, global moderates A, B, and C, and more extreme alternatives D and E. The party affiliations are A and B in one party, and C,D,E in the other. Alternative D is solidly in the middle of its party, and alternative E is at the extreme.

The actual profiles are as follows. However, these are not known.

A>B>C>D>E 24%
B>A>C>D>E 24%
C>D>A>B>E 11%
C>D>B>A>E 11%
E>D>C>A>B 7.6%
E>D>C>B>A 7.6%
D>E>C>A>B 3.7%
D>E>C>B>A 3.7%
D>C>E>A>B 3.7%
D>C>E>B>A 3.7%

If you look at these profiles carefully, you'll see C is a Condorcet winner. However, this is an IRV election so polls will be about round results and what would happen after eliminations, and C's Condorcet status is not reported as such.

The polls state: A and B are the frontrunners for the first round, with C, C3 and C2 following. C2 voters are likely to have C or C3 as their second choices. Almost all C3 voters have C2 as their second choice, with C as a distant third. A and B voters are likely to stay within their party, but could tolerate C. If forced to choose, C voters strongly prefer C2 over C3, but might possibly break with their party if their only in-party choice is C3.

Our voter Joey is pretty undecided about A and B, liking both, but very much anti C,D,and E. So Joey takes the poll data and considers the likely outcome:

First count, A:24%, B:24% (too close to call), C:22%, C2:14.8%, C3:15.2%.
Status: no winner, C2 eliminated

Poll say C2 votes will split evenly between C and C3.

Second count: A:24%, B:24% (too close to call), C:29.4%, C3:22.6%.
Status: no winner, C3 eliminated.

Polls say the initial C3 preferences were C3>C2>C, and the initial C2 preferences were split between C2>C3>C and C2>C>C3. With C2 already eliminated, all of C3 votes go to C.

Third count: A:24%, B:24% (too close to call), C:52%.
Status: C is the winner.

Given these predictions, Joey might decide to change his honest vote from A>B>C>C2 to C2>A>B>C, and encourage some of his like-minded voters to do the same. If enough of them collude, they might prevent C2 from being eliminated in the first round, causing C3 to be eliminated so that in the second round, with C2 picking up all the votes from C3, there will still be no winner and C will have the lowest vote count and be eliminated.

If 0.5% of the A or B voters implement this strategy, the IRV election would run:

First count, A:23.75%, B:23.75% (too close to call), C:22%, C2:15.3%, C3:15.2%
Status: no winner, C3 eliminated, C3 votes all go to C2.

Second count, A:23.75%, B:23.75% (too close to call), C:22%, C2:30.5%
Status: no winner, C eliminated, C votes split among A,B,C2

Polls are unclear here but all three remaining alternatives are expected to
pick up between 5-10%.

At this stage, with C and C3 eliminated, it is unlikely that there will be a third count winner. But the key point is that both A and B are expected to be able to defeat C2. This means if either A or B is eliminated in the third stage, the remaining alternative will win in the fourth stage. And if by some chance C2 is eliminated, the final round will be between A and B, both of which Joey and friends prefer over all others.

The big problem with this scenario is the poll claim that A and B are frontrunners because they get the most votes in the first round. However, IRV is hard to predict and it is quite possible polling agencies might be wary of predicting beyond the first round when the elimination choice between C2 and C3 is so close.

In any event, I hope this is a reasonable illustration of the manipulability of IRV. (Of which I am not a fan.)

rob

@Jack-Waugh said in Simulating Voting Strategies:

What if the voter favors both front runners and opposes everyone else? Will that voter have an incentive to vote other than "honestly" in IRV?

First of all, I asked for clarification on your previous questions, and you responded with a different question. Ok.

Secondly, what does this have to do with voting simulation? This just seems a general voting theory question.... almost a non-sequitur. Maybe if I understood more about where you are going with this line of questioning.

I also have to ask, in your scenario, are you suggesting that the voter likes the two front runners exactly equally? Like, exactly exactly? Are you also suggesting that the two front runners are, without question, going to be the two front runners? If both of these are true, the voter has very little incentive at all. They might just not bother voting, which I wouldn't blame them for. They like each candidate equally, so they could flip a coin as to which to put first. It is no different than if only two candidates are running under conventional (i.e. majority/FPTP) voting, and you like them both, and equally. Big deal. You'll be equally happy with either possible outcome. I don't see a problem.

Bringing it back to simulators, in the simulator I was working on and linked above, this can't really happen. Well, for it to happen you'd have two floating point numbers, which are essentially random, be precisely the same.... which is unlikely in the extreme. While I suppose it isn't quite so unlikely for a human to describe their preferences regarding two candidates as being "exactly the same", I just don't see this as a problem.

(that's not to say I like IRV, I don't, but this particular problem that your question implies is not really a problem, in my opinion)

tec

@Jack-Waugh Just a clarification. My post about Warren D. Smith's Range voting paper was in response to this request for strategic algorithms to simulate. Next time I'll be sure to "reply" to the post I'm replying to. Sorry for any confusion.

tec

@Jack-Waugh My apologies. I did not notice that your question about a voter favoring both front runners was directed to @Rob. I mistakenly thought it was directed to me based on a strategy WDS proposed in his paper for IRV simulations.

The WDS strategy assumes the two front runners are significantly distinct and any voter tempted to vote strategically would have strong preferences. If I recall correctly, the WDS strategy for IRV (Strategic Hare STV) was to give the maximal rank to the better of the two front runners and the worst rank to the lesser front runner, then use a moving average to fill out the ballot by giving the highest remaining rank to the next most likely alternative that was better than average and the lowest remaining rank to the next most likely alternative that was worse than average.

That strategy is certainly codable for a simulation, but it also seemed like a direct lead-in to your question about a why voter that liked both front-runners would vote strategically, and framed the question in the real world. Hence my response. Hopefully, it is at least an interesting scenario.