[EM] Quantifying manipulability

[Elisabeth Varin/Stephane Rouillon]

Steve --

> When I say she is "rewarded," I mean that her second choice is elected.
> When I say she is "punished," I mean that her last choice is elected.
> When I say she is "neither" punished nor rewarded, I mean that neither her
> first nor second choice is elected, due to either a tie for first place or an
> otherwise indeterminate outcome.
>

I would simply consider that in 3 candidates race like this one (A, B, C), a voter would be
"rewarded" by electing is first choice, and "punished" when the third choice is elected.
If we use an objective function that describes the gain and loss obtaines by truncation,
we can measure the esperance of gain and compare the mean gain or loss obtained
by truncation. A +1 objective value for each rank amelioration would fit.
Thus in your example the reference tie could be considered as having a zero value
(1/3 + 0/3 - 1/3 = 0), a first choice win  a 1 value, a second choice win a 0 value and
a third coice win a -1 value.

The probleme is to do this job for a umonguous number of cases.
Josh, still a computer expert? How many different cases could you simulate?

Steph.
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