Tuesday, January 17, 2012

The Unexamined Assumption

I've been recently reading some blogs from very good statisticians and modelers, who've made me question things EVEN MORE than I normally do.

So when I today read two columns here and here about how voters would consolidate if other candidates were gone, I let my skepticism run wild.

These columns (and some of my own forecasts) read data from a poll that that asks 'Who is your second choice candidate' and assume that the voter reading this question was thinking "If for ANY REASON WHATSOEVER, I decided not to vote for the guy I listed a few moments ago as my first choice candidate, when the date and time comes to actually vote, I will vote for person I am about to write down as my second choice."

Even though, in reality, there are many possible scenarios for why and how someone decides to change their mind. It is HIGHLY unlikely that the authors of these two articles, myself when I was making some forecasts, or any randomly chosen pundit, will have considered all of the following and assigned various conditional probabilities to each one (more likely they said it was 100% chance it is scenario Z... Z being which ever one of these or others I didn't write down, appeal to them most).

So, what are some scenarios:

1) Candidate 1st Choice may withdraw from the race (or scenario 1B appear to be unlikely to do well on election day) before I actually vote
and I think the candidate 2nd choice has similar enough values to candidate 1st choice

2) By the time I vote, candidate 1st choice may look highly unlikely to do well in the vote, in which case I will go with candidate 2nd choice because he will likely do well and he is tolerable (and I *may* even tell acquaintances that I voted for him)

Both scenarios are plausible. What percentage of scenario 1 people are in a given cross tab of 1st choice vs. 2nd choice in some poll will vary widely depending on what other characteristics the actual candidate 1st choice and candidate 2nd choice have and the probability that the person will vote for the second choice.

No polls provide us with this information. So each reader makes their own (likely unconscious) decisiion.

Just to make it less abstract, consider that the election is this Saturday's SC primary, Santorum is candidate 1st choice and in scenario 1 candidate 2nd choice is Gingrich whie in scenario 2 candidate 2nd choice is Romney.

Going back to the abstraction, there are other plausible scenarios the pollee had in mind when they made their answer.

3) I don't know anything about any of the other candidates except that I've heard candidate 2nd choice's name a lot, and I feel obliged to vote for someone. I'll chose candidate 2nd choice if at the last minute candidate 1st choice withdraws (or scenario 3B - if I hear at the last minute bad news from TV/my friend/a false rumor in my email or mailbox)

4) I'm tired of waiting for this automated poll to end, and I don't really care about this 2nd choice question, so I'll just give them this answer for 2nd choice quickly so I can finish the poll.

5) Candidate 1st choice is my first choice today, though candidate 2nd choice was my first choice last week, and I might go back to him

6) Candidate 1st choice is actually my significant other's REALLY favorite first choice and he/she may not be able to vote, so I'll be nice and vote it for them, but if they are able to vote, then I will vote for candidate 2nd place because they seem pretty good.

I am sure creative minds can think up a dozen more examples that at least some pollees had in mind when they cast their 2nd choice 'vote' in the poll that has no actual binding requirement/lasting effect on their actual vote.

The point is, don't be so sure you know how voters will change their vote. At least not if you are going to believe this is going to cause a double digit swing between today's polls and Saturday's actual voting.

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