[EM] simulating an Approval campaign/election

[Russ Paielli]

As a followup to my post this morning, I'd like to make a few 
suggestions about effects to consider in simulating the dynamics of an 
Approval campaign and election. I'd consider writing a simplified 
simulation myself if I had time, but I don't. I have developed aerospace 
control systems and simulated them in the past (and published journal 
papers on them), but I've never simulated anything involving elections. 
If what I am about to suggest has already been done, please let me know.

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