[EM] Range Voting in presence of partial information of a certain character

[Kevin Venzke]

Hi Forest,

--- En date de : Mar 18.5.10, fsimmons at pcc.edu <fsimmons at pcc.edu> a écrit :
> Suppose that you were voting a range ballot and all you
> knew was that candidate  X  was very likely to 
> win or be tied for first place.  Then you should give
> max support to each candidate that you prefer over X, 
> and zero support to the candidates that you like less than
> X.  But what about X ?  How much support 
> should you give to alternative X ?
> 
> If you knew which candidate Y was most likely to be tied
> with X, then you would give X full support if you 
> liked X better than Y, and no support if you liked Y better
> than X.  But we’re assuming that this 
> information is unavailable.
> 
> So all we know is that X is very likely to either win or be
> tied for first place in the range count. Obviously 
> if X is your favorite, you should give X top rating, and if
> X is your most despised option, you should rate X 
> at minrange.  Suppose that X was halfway in between
> your favorite and worst, i.e. you would be 
> indifferent to having X or a coin flip between Favorite and
> Worst.  Then it seems natural that you would 
> give X a rating half way between the max and min range
> values.

I don't know, I don't think you would want to do this unless your math
was such that you could find that your vote for X is irrelevant. For
example if you rate W 10, X 5, Y 0, and assume W and Y to have equal win
odds, then no matter what X's odds are, your expectation for the 
election is 5. So strategy says it just doesn't matter how you rate X.

But suppose you rate W 10, X 5, Y 0, and Z 9, and guess that X has a
94% chance of winning/tying and everyone else has 2%. Then your 
expectation is .2+4.7+0+.18 = 5.08 and X should get the zero rating.

Kevin