[EM] Approval Voting vs Instant Runoff Voting:

[LAYTON Craig]

Hi Bart,

you wrote:

>You're not arguing that a voting system should "guarantee a majority
>winner", are you?

No.  It's impossible to guarantee a majority winner.  However, a good
Condorcet system (Cloneproof SSD & Shulze beatpath winner are the popular
ones at the moment, and I must agree that they're the best) will guarantee
at least one majority (in the sense that a majority of voters prefer the
elected candidate to another candidate that is running), and attempt to
minimise the overruling of other majorities.  Approval doesn't do this.
Approval can elect a candidate that isn't preferred by a majority to any
other candidate.  This seems fairly anathema to the concept of democracy to
me.

>If you are departing from the four-equal-frontrunner example above, then
>I would expect the vast majority of voters to bullet vote, at least
>present-day U.S. elections where two parties dominate.  Assuming most
>voters, at least for the near future, continue to prefer major party
>candidates, then I would expect them to bullet vote.  Sorry, but I
>really don't see this as a problem.

Yes, Approval does well when there are only two candidates with a chance of
winning, but then, so does IRV.  In fact, IRV does better, because it
ensures that the most popular of the two candidates wins (which would also
be the Condorcet winner).  But, as we all know, IRV does terribly when there
are more than two popular candidates.  Approval isn't too good in this
territory, either.

> > American, I guess it would be a race between a democrat, republican,
reform
> > and then someone even more right wing than that.  In Australia, I can
> > imagine the race to be between Labor, Liberal, National and One Nation.
In
> > that order, my sincere estimated utility value (out of 100) would be
> > something like 100, 25, 20, 0.  It would not be unreasonable to suggest
that
> > I vote for only the "100" in such a scenario.
>
>I agree -- especially since your mean utility for the four candidates is
>around 36.
>  
>It's interesting that you were able to arrive at the correct strategy,

It's only the correct strategy if the four candidates have a reasonably
equal chance of winning.

>apparently without resorting to the math.  I suspect that most real-life
>voting situations will be similarly obvious.

The 0 info strategy math seems fairly straight forward, even to me, and
generally corresponds to intuitive choice.  I'd be interested to get an idea
of what the optimum strategy would be in a more complex scenario.

This question is open to all the strategically minded posters; Say with the
above utilities (100, 25, 20, 0 - assign A,B,C,D respectively).  One opinion
poll shows (and, being an approval election, these are approval polls so
they show the predicted winner), that A will get 36 percent of the vote, B
will get 40, C will get 45 and D will get 44.  You know that there is some
error in opinion polls; say that you are reasonably sure, based on the
poll's claims, that there is a 90% chance that the opinion poll will be
within 5% of the actual vote (that is, 90% chance that A will get between 31
and 41%), and that it is more likely to be closer to the poll than further
away (more likely to be 36% than 41%, but we don't know how much more
likely).  How should you vote?