[EM] "small case" study

Stephane Rouillon stephane.rouillon at sympatico.ca
Wed Sep 1 05:47:34 PDT 2004

Maybe I was not clear.
I consider a small case to be a stusy about of all possible ballot sets
that a small number of voters (3 or 4) can produce. Then for each election
method we would evaluate the esperance of gain of unsincere strategies for
A small case is not an example.
This "small case" is more a huge work...

Adam Tarr a écrit :

> Stephane Rouillon wrote:
> >Maybe I need more mathematical support on this but, even if I agree with
> >Mike, I evaluate the number of time I would have to bury my favourite in
> >order to get it elected with IRV far less than the number of time I could
> >lose him by not setting properly my approval cut-off with approval. It is
> >a matter of odds (probability).  Could someone evalute those, even just
> >for a small case?
> OK, a small case follows.
> The names of the candidates are with respect to your preferences.  The
> breakdown of voters is uncertain, but it is EITHER:
> 35% Worst
> 5% Worst>Compromise>Favorite
> 12% Compromise>Worst>Favorite
> 13% Compromise>Favorite>Worst
> 35% Favorite>Compromise>Worst
> OR,
> 30% Worst
> 5% Worst>Compromise>Favorite
> 12% Compromise>Worst>Favorite
> 13% Compromise>Favorite>Worst
> 40% Favorite>Compromise>Worst
> The difference, of course, is that in the first case, you lose the second
> round runoff in IRV, and in the second case, you win it.
> In IRV, if you really hate Worst, you have good reason to sell out Favorite
> and put Compromise in first.  This causes Favorite to lose in the first
> round, so that Compromise wins the runoff.  This is the classic "lesser of
> two evils" scenario.
> In Approval, I can always vote for favorite, but the question is whether I
> approve compromise as well.  It's a very similar dilemma, although I don't
> have to actually sell out my favorite.
> Now, here's the twist.  Say the second situation is the
> reality.  Furthermore, suppose that 8% of the 40% in my faction decide to
> sell out favorite (and a similar 1% of the 5% in the W>C>F faction).  So
> the votes, in IRV, look like:
> 30% W
> 4% W>C>F
> 13% C>W>F (including 1% insincere)
> 21% C>F>W (including 8% insincere)
> 32% F>C>W
> So, favorite gets eliminated in the first round, and compromise wins, and
> that 8% of the electorate that sold out Favorite spends the next four years
> feeling like idiots.  Now, suppose we have the same number of "double
> approvers" in the Approval election.  I'll assume a fifth of the
> compromisers (3% on each end) also approve their preferred wing, just like
> for the other factions.  So, with an equal amount of "compromising" going
> on, the votes are:
> 34% W
> 4% WC
> 19% C
> 11% FC
> 32% F
> Now, despite the same amount of "favorite betrayal" as in the IRV example,
> Favorite still wins.  So here we have a pretty good argument that approval
> is MORE forgiving in this case than IRV.  In general, it takes twice as
> much mistaken compromising to sink the stronger wing candidate in approval
> versus IRV.
> And one last note: this whole strategy problem is trivialized in
> Condorcet.  Just vote sincerely, and go home.  As such, this example makes
> a good case for my Condorcet>approval>IRV>plurality preferences.
> -Adam
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