# [EM] Basic Arrow's Theorem Question

Stephane Rouillon stephane.rouillon at sympatico.ca
Tue Apr 22 19:07:07 PDT 2003

```Alex,

could we design a measure of how bad and how often we have to deal with
Arrow's problem for a given system?

I would like to compare such a criteria for FPTP, SPPA, STV and MMP...
Note that I want to compare multiple-winners election methods.

Steph

Alex Small a écrit :

> I'm not sure what your question is, but your example focuses on
> competition between candidates and the dynamics of a debate.  Arrow's
> Theorem doesn't address the fact that adding more candidates to a debate
> will change the types of questions discussed and perhaps change people's
> preferences.
>
> Arrow's Theorem addresses this situation:  "OK, assume that every voter
> has made up his or her mind about the relative merits of WN, PS, and BBQM.
>  If you only give them ballots with PS and BBQM listed, say that PS wins.
> Then say we add WN and they all vote again.  This time, BBQM (the old
> loser) wins, rather than PS (the previous winner) or WN (the new
> challenger)."
>
> Arrow proved that you can't design a system that avoids that problem if
> you use ranked ballots (assume no equal ranking or truncation for now),
> you don't have a dictator (sorry, Ashcroft...), and your method always
> picks the unanimous first choice of the voters if such a candidate exists.
>
> Arrow says nothing about that third candidate perhaps changing the terms
> of the debate, because that would change voter preferences.  The
> assumption is that voter preferences stay fixed.
>
> >
> > OK, If everyone thinks A is better than B, A beats B. Fine.
> >
> > If C enters the race, no ones opinion of the A-B pairing changes.
> >
> > Hmmm.
> >
> > Sample Race, with imaginary figures.
> >
> >
> > 1.
> > PloddingSafe and BrashBrightQuestionMark enter a race.
> >
> > 2.
> > PS and BBQM debate.
> >
> > 3.
> > People decide who they like in the PS-BBQM pairing.
> >
> > 4.
> > WingNut enters race.
> >
> > 5.
> > PS, BBQM, and WN debate.
> >
> > 6.
> > WingNut makes PloddingSafe lose cool! red in the face! loss of words!
> > more?
> >
> > 7.
> > Some PS supporters think...
> >     hey, what gives!
> >     Maybe BBQM is really the PS candidate!
> >     After all, BBQM doesn't blow up around WN
> >
> > The entry of C(WingNut) into the race has changed the A-B pairing? Or is
> > that something else entirely.
> >
> > Thanx.
> >
> > Thing is, remember, third party candidates tend to be extreme and always
> > hurt the candidate from their side.
> >
> >
> >
> >
> > ----
> > Election-methods mailing list - see http://electorama.com/em for list
> > info
>
> ----
> Election-methods mailing list - see http://electorama.com/em for list info

```