[EM] Responses to some of Forest's ideas

[Richard Moore]

Forest Simmons wrote:

> The results of these simulations would depend on what strategy you used
> for zero info Approval. Did you use above mean, not below median, above
> midrange, above largest gap, some combination of these, or Richard's
> optimal method?


Forest,

Which method? The only optimal zero-info method (from a 
utility-expectation viewpoint) that I know is the above-mean 
strategy, valid for large populations. The only other 
Approval strategy I remember proposing, besides the "neural 
network" strategy of voting whichever way "feels" best, was 
an approximation for small populations. I never really 
determined how good that approximation is, so I don't 
consider it optimal. Is that the method you mean?

At one time I thought that "above largest gap" was a good 
strategy, and that's probably what a lot of people's neural 
networks will do. Of course it's not optimal but it does 
suggest a way of voting with a high comfort (or low regret) 
level.

I've always believed, as you do, that the effects of 
strategic voting in Approval are benign. My reason is that 
if you shift your threshold to include one more middle 
candidate, the worst you can do is cause one of your middle 
candidates to beat your favorite, which is a lot better than 
some methods where strategic voting can backfire and shift 
the result to your worst nightmare. In other words, you at 
least have the power to minimize your worst regret. In IRV
(to pick on our favorite demon) you don't have that luxury.

Richard