# [EM] Quantifying manipulability

barnes99 barnes99 at vaxa.cis.uwosh.edu
Thu Dec 5 16:48:30 PST 2002

Here is my analysis of the following profile, up to this point:

> > 1 ABC
> > 1 ACB
> > 1 CAB
> > 1 CBA
> > 1 BCA
> > 1 BAC

All methods agree on a complete tie for this profile, of course.
If one of the voters reverses her top 2 candidates (for example, A>B>C
switches to B>A>C), she is either rewarded, punished or neither, by the
following methods as indicated:

Plurality: R
Borda Count: R
IRV: N
Pairvote: N
Copeland: R

If she rotates her sincere second choice up to first, moves the sincere last
choice up to second, and puts her sincere first choice last (for example,
A>B>C rotates to B>C>A), she gets the following rewards, etc:

Plurality: R
Borda Count: N
IRV: N
Pairvote: N
Copeland: N

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.

Therefore, as you can see, according to my analysis thus far, these methods
rank as follows from most to least manipulable:

Plurality: RR
Borda Count: RN
Copeland: RN
IRV: NN
Pairvote: NN

OR

Plurality > Borda~Copeland > IRV~Pairvote

Can anybody go further with this analysis?

SB

PS: While I'm at it, let me make a correction to my previous message. The 2nd
sentence of the following paragraph, change the word "sincerely" to

"If too many people insincerely put Nader between Bush and Gore, and voted

> barnes99 said:
> > The Borda Count will  punish an insincere vote in some cases, and that is
> > actually an incentive to  vote sincerely. If too many people sincerely
> > put Nader between Bush and Gore,  and voted either Bush>Nader>Gore or
> > some information to successfully manipulate the  BC,

Steve Barney

Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/hare.htm>.

Did you know there is an web site where, if you click on a button, the advertisers there will donate 2 1/2 cups of food to feed hungry people in places where there is a lot of starvation? See:
<http://www.thehungersite.com>.

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