Forest Simmons simmonfo-at-up.edu |EMlist| wrote:
Departing from Strategy A, we offer the following refinement in the same spirit:
For each candidate C, if you think the winner is more likely to come from the set of candidates that are worse than C than from the set of candidates that are better than C, then approve C, else don't.
Now that's an elegant way to state the strategy.
This neatly takes care of all of the cases, and agrees with Strategy A whenever there are two definite frontrunners.
Perhaps if Russ were to study this strategy he would see the continuity between the two dominant party case and the general case that he is worried about.
Perhaps some of the folks here missed my point about Approval strategy. Well, at least one person has, but he is a fruitcake.
Two different questions can be asked about any voting system:
1. What is the best voting strategy? 2. How effective is the best voting strategy?
The fruitcake can't distinguish these two questions, but perhaps others can.
Let's apply these questions to plurality as an example. The strategy is simple to formulate, but how effective is the strategy? It is very effective if you prefer one of the two major parties, but otherwise it is not very effective.
You've stated what is perhaps the best strategy for Approval, but how effective is that strategy? Well, in some cases it may be very effective, but in other cases it may not be.
For example, what if *three* parties are equally popular? Let's take the classic Democrat (D), Republican (R), and Green (G) case. Suppose they are approximately equally likely to win. And suppose your own order of perference is G>D>R. Who do you approve?
Well, you could play it safe and approve both G and D. But then you will be disappointed in your choice if it turns out that G could have won had more G>D>R voters not approved D.
Then again, you could be bold and only approve G. But then you will be even more disappointed if R wins but D had a good chance if only more G>D>R voters had approved D.
Do you see the dilemma here? The problem is not that you don't have a formula to guide your strategy. The problem is more *fundamental* than that. The problem is that *no* formula can help. Your best strategy is more or less a coin toss.
And we haven't even got to the case of four competitive parties.
Incidentally, Approval strategy seems to be more sensitive to polling results more than most other methods. In plurality, pre-election polling results might affect whether you bother to vote at all, but they are not likely to swing your vote one way or the other. The same is not true of Approval. In Approval, your strategy is likely to depend strongly on pre-election polling results, particularly if several candidates are competitive. So what, you ask? Well, has it occurred to anyone that pre-election polls can easily be rigged? Its something to think about (but not if you are a fruitcake).
--Russ
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