[EM] [EM} FPTP is not strategy proof!!!

[Stephane Rouillon]

Plurality is really easy to manipulate:

suppose sincere preferences
42: A>B>C
44: B>A>C
14: C>A>B

If I am a C>A>B supporter and I have an exact knowledge of the situation,
Instead of voting for C, I would vote for A to make him win instead of
B. Reversely, if I do not have enough information, I could make A win instead
of C.

This is a clear strategy problem. I do not understand how you can say FPTP is
strategy proof. And I particularly find Mr. Monroe design of a class of
strategy
problems that FPTP passes useless when it does not pass other classes.

All electoral systems have strategy-issues (Arrow's theorem), to compare the
different systems,
you would need a measure of the probability strategy cases rising and a
measure
of the gravity of their consequences. Sum up all that you could obtain a mean
deviation per election in term of the number of ranks stolen by the winner
(for single-winner
systems). Calculus are complex because you have to take in account the impact
of
the number of candidates, the number of voters, the real distribution of
preferences,
and finally, definitively not the least, the fraction of each block of voters
(with the same
preferences) that believe a particular scenario will occur.

To get back to my example,  B will win unless more than 13 % of the C>A>B
voters
believes that C has no chance winning and decide to act on it.

As long as an electoral method issue can be modified by believes, it is not
strategy-proof.
You only need to make voters believe "your" way.

Hence the best test I can actually think of to asses an election-method
quality is the following:
Suppose a majority of voters wanting a specific candidate.
How many of those voters do you have to make believe something false (about
initial
sincere preferences) to finally steal the election.

Still, it leads to gigantic combinatorial problems and we should take in
account how much
false is a pairwise comparison reversal compared to a bullet ballot change...
However limit cases study could indicate some ranking of electoral methods
"unstrategizable"
levels...

Steph, please comment...

Markus Schulze a écrit :

> Dear James Green-Armytage,

<snip>

> ******
>
> You wrote (19 Aug 2003):
> > Could it be possible to design a version of Condorcet that is more
> > strategy-proof than beatpath or ranked pairs?
>
> That depends on what you mean with "strategy-proofness". For example:
> Mike Ossipoff and Russ Paielli consider invulnerability to "compromising"
> (i.e. ranking a candidate insincerely higher to make him win) to be not
> a strategical problem. Therefore, they consider FPP to be strategy-proof.
> The only reason why they reject FPP is that FPP can find an "obviously
> wrong winner".
>
> Russ Paielli wrote (6 Aug 2003):
> > Plurality is also "extremely difficult to manipulate" in this way,
> > isn't it? What kind of "offensive strategy" could you possibly use
> > in plurality? None that I can think of.
> >
> > (...)
> >
> > The one and only possible way of helping the Libertarian (or any other
> > candidate) win is to vote for him. But then you are voting sincerely,
> > hence you are not "manipulating" anything. Plurality is therefore
> > beyond manipulation.
>
> What I wanted to say is: From a given point of view, it is rather
> subjective which strategical problem (e.g. truncating, burying,
> compromising, pushing over) is more offensive, more undesirable,
> more drastic, more implausible, more counter-intuitive, etc..
>
> Markus Schulze
> ----
> Election-methods mailing list - see http://electorama.com/em for list info