[EM] Responses to some of Forest's ideas

[Richard Moore]

Rob LeGrand wrote:

> A while ago, Craig wrote:
> >  9 A>B>C>D=E=F : 100>90>1>0=0=0     : ZI AB  : St AB
> > 38 B>D>A>C=E=F : 100>52>51>0=0=0    : ZI BDA : St B
> > 40 C>B>A>D=E=F : 100>85>70>0=0=0    : ZI CBA : St C
> >  9 D>C>B>A=E=F : 100>10>9>0=0=0     : ZI DC  : St DC

Actually the ZI vote for the 4th group is D only. Won't make a difference, though.
We'll get to the strategic votes in a bit.

> >  4 E=F>A>B>C>D : 100=100>90>12>10>0 : ZI EFA : St EFA
> >
> > Undefeated (definite) Condorcet Winner is B.  Zero info approval winner
> > (taking both mean and median into account) is A.  Strategic approval winner
> > is C.  It seems pretty clear that I've used optimal strategy, although I
> > haven't done all the math.
>
> I'd say B and C would shape up to be the frontrunners, and the best strategic
> approval votes would be:

It could be argued (from the ZI scenario) that A and B are the front-runners. But
since most of the common supporters for A and B in the ZI case prefer B, A will
lose a lot of support if those voters use "A and B are front runners" as the basis
for their strategy. That would make B and C the new front runners, and the group
of 38 could recalculate their strategies, so A might regain some support. Since it
is very difficult for voters to take into account the psychology of the other
voters,
most likely everyone will see B as the strongest front runner, with A and C about
equally likely to challenge B (it won't be clear which one until the group of 38
makes up their mind -- and they may not all reach the same conclusion anyway).
Therefore one approximate strategy would be to do the mean calculation as in ZI,
but with weightings assigned to the candidates (e.g., B has a weight of 2, A and
C have weights of 1, D has a weight of 1/2, and long shots E and F have weights
of zero).

Another factor is that if the third group votes C only, then D has a fighting
chance
and could tie with B for first place. The only way for D to win with reasonable
strategies is by winning a tie-breaker. D is unlikely to get this far, because if D
is
ever strong enough to be seen as a front runner then negative feedback from the
BDA voters will correct this.

But let's go with Rob's assumption and see what we get:

>  9 AB

I agree.

> 38 B

This isn't the only likely strategic vote from this group. It comes back to the
question Roy raised about weak information vs. strong information. If we
have strong information, for instance, if we can see the ratings above before
we vote (or have a highly trusted poll representative of the actual voters),
then these voters will vote B only. If their information is limited to "B and C
are front runners", then they'll include at least one of their next two choices
as insurance. Also, even given the full ratings, can they assume the other
voters will have the same information, or that the other voters are strategic
voters? If they assume the first group of 9 voters and the last group of 4
voters can't be relied upon for help in electing B, then they will be inclined
to vote BDA.

Also note that if only relative rankings are provided for the other voters, you
have much weaker information than the full ratings given above. Of course, if
the information is from a poll, then rankings are less likely than ratings to be
distorted by the poll's participants.

> 40 C

I agree.

>  9 DC

Given that the second group might give some support to D, making D a credible
(though weak) candidate, and given the large DC utility gap for this group, they
could play the odds and vote D only.

>  4 EFAB

Again, the utility gap might be enough to make this group ignore the front runners
and vote EFA.

Assuming the second group votes BDA, and the last group votes EFA, I see A
as the winner.

> Whichever two candidates emerge to be the frontrunners, B should be one of them
> and win.  Won't the strategic approval winner always be the sincere Condorcet
> winner when one exists?

The lesson is, there really isn't such a thing as strong information in an Approval
election,
unless you are able to peek at the other ballots before you cast yours. I recommend

voting ZI strategy in Approval elections for this reason. Or vote according to the
weighted ZI strategy I suggested, if you have a reasonable idea of the other voter
tendencies. You won't always end up with the CW or even the highest SU winner if
everyone votes this way, but you do tend to end up with a good compromise candidate

even if the electorate is strongly divided.

BTW, I worked out the weighted ZI strategy results, using the weights I suggested
above:

9      AB
38    B
40    CB
9      D
4      EFA

which results in a win for B.

One last comment on this example. Note that each group consists entirely of clones.

Every voter in a group has not only the same rankings but the same ratings. It is
far more likely that you will have groups with identical rankings but considerable
variations in ratings among their members. Thus not all members of a group will
vote
the same in a given situation. In a real election, there will be an even richer
diversity
in that many more of the possible candidate rankings will be present. This
diversity
of opinion is frequently ignored in our simplistic examples, and (at least in the
case
of Approval) it is actually a stabilizing influence.

Richard