In plurality elections, the polls may have an effect on turnout, and they may have an effect on how many voters decide to case "protest" votes for a minor party. If the race between the big two is not close, then fewer voters will bother to vote and more will cast protest votes. However, if the race between the two major parties is close, the poll results themselves are unlikely to cause voters to switch from one side to the other.
Approval Voting differs from plurality in that voting strategy is much more dependent on expectations of candidate support. As you all know, a voter's optimal "cutoff point" will often depend strongly on those expectations. Those expectation are obviously very dependent, in turn, on pre-election polling results.
That dependence creates very complicated feedback loop. Voter preferences affect poll results, then the poll results affect voter preferences. Even if we assume that all voters maintain a stable preference order throughout the entire campaign and merely adjust their cutoff point in response to poll results, the dynamics of this feedback loop is high-dimensional and could be extremely complicated.
To simulate the dynamics of this feedback system, one must first realize that polling itself will be very different from what we are currently accustomed to. Pollsters now simply ask potential voters which party/candidate they intend to vote for. But when Approval comes along, they will need to ask which parties/candidates (plural) they intend to vote for. Aside from the massive general confusion, condsider that the smart voter can't really make that decision until he has some idea what other voters will do.
So we have a potential catch-22 here. The question then becomes whether the poll results will stabilize and converge to the actual election results (at least approximately) before the actual election occurs. In other words, do the polling results tend to converge to the actual election results, do they converge to the wrong result, or do they oscillate wildly (and perhaps chaotically) so nobody has a clue by election time what to expect from the other voters?
For any simulation of Approval Voting to be significant, several key effects need to be modeled beyond the standard models of voter positions on a political spectrum. For example, a model is needed for how voters reply to pre-election polls. That could vary depending on how close the actual election is. Even if we assume that all voters maintain a stable preference order throughout, a model is needed for where voters draw the cutoff line when responding to a poll. How this should be done would be largely a matter of guesswork since voters have no incentive to think hard about what their actual cutoff point will be. And even if they do think hard, it is bound to change as new poll results come in. The "strategy" for answering a pollster is certainly not the same as it is for actual voting.
OK, now assume that a poll-response model is available. Voter strategies then need to be assigned. Strategies have been discussed at length on this forum, but that is a relatively small part of the simulation problem. The harder part will be to determine what percentage of voters will use each particular strategy. That will perhaps require a study in itself. As a first cut, each strategy can simply be tried separately for all voters, of course. If they all yield similar results, than that part of the problem simplifies. But if they don't, it becomes more complicated.
OK, now we have models for (a) voter replies to pollsters, and (b) actual voter strategies for the real election. To run the simulation, we need to simulate a series of pre-election polls leading up to the actual election.
As a baseline test, this could all be done assuming absolutely no uncertainty in the polling results (except the indecision already discussed about where respondents draw their cutoff line). This might give a clue about stability in the absence of other uncertainties.
After that, things start to get more interesting. Now we need to model uncertainties in the poll results. Remember, polls only sample a tiny fraction of the electorate. Also, some percentage of respondants lie just for kicks, and something like 40% either never answer the phone or tell the pollster where to shove it.
OK, so how do we model the polling error? That could be a study in itself, of course, but we'll keep it relatively simple with a guassian model, characterized by a mean and variance. Many different combinations need to be tried. I think a random mean error of up to, say, 5% needs to be tried (in many different combinations, of course).
After all that (if we haven't retired yet) we can think about modeling actual changes in voter preference order due to something really radical such as ... a candidate saying something? Oh, yes, I almost forgot that candidates sometimes try to change voter's minds! That "extra" dynamics needs to be thrown in on top of all the other underlying dynamics discussed above. This is comparable to the natural and forced dynamics of an aircraft, I suppose.
Does anyone still think this problem is simple? Does anyone think they can prove that the polling results will always be stable, or under what conditions they will be stable? If so, I'd like to see the proof. I'm not claiming it can't be done. I'm just wondering if anyone really understands the problem.
--Russ
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