[EM] Unranked-IRV, Cumulative, and Normalized Ratings

[Martin Harper]

It seems pretty clear that at some point you have to make a trade-off 
between electing the candidate with the highest SU, and ensuring that 
your method has low strategy. However, its unclear at what point you 
have to start making a trade off - it is conceivable that there are 
methods out there with less strategy which elect higher SU candidates - 
and Cranor's may be one of them.

It'd be interesting to speculate on where exactly the limit is. I wonder 
if it would be possible to formulate some kind of equation linking 
quantity of strategy with percentage SU achieved with sincere votes - or 
better yet to find the maximum achievable SU with actual votes (IE, 
taking strategy into account). Beyond my powers, though.

The other question is how we choose in which direction to miss the 
maximum SU on sincere votes, and so ensure that our method is 
strategy-free. Is it better to be a little below on many, or much below 
but only in rare cases? Is it better to elect a non-optimal extremist or 
a non-optimal narrow centrist? Etc...

Election methods does seem to be the study of what is impossible 
sometimes, with Arrow's Theorem, this thing, and the 
strategy/determinism dilemma.

Forest Simmons wrote:

> This is more of a query about Lori Cranor's method than anything else.
> 
> If it really gives no strategic incentive for distorting ratings, it
> sounds like the ideal way to use CR ballots.
> 
> Here's what puzzles me. On the one hand, it seems like any method like Ms
> Cranor's that uses CR ballots to formulate optimal Approval Strategies
> should be able to do so in a way that would give the win to the candidate
> with the greatest average rating.
> 
> If that is the case, then it seems like any strategy that would improve
> the average rating of your favorite on the CR ballot would be tempting. In
> other words, one would be tempted to distort ratings. 
> 
> On the other hand, if the method doesn't give the win to a maximally rated
> candidate, then it probably isn't much better than plain old Approval in
> social utility.
> 
> Can you shed any light on this?
> 
> Forest