[EM] [CES #8565] Re: The chicken dilemma, median systems, and the pivotal voter

[Jameson Quinn]

I don't think I've expressed my "pivotal voter" argument very well.
Warren's response clearly points to some holes in what I've *said*, but I
think my underlying argument is still firm.

So before responding point-by-point, let me try again to say what I'm
trying to get at.

Assume a chicken scenario: a plurality-winner condorcet-loser "opposition"
X, and two near-clones Y and Z, of whom Z is the Condorcet winner.
Typically, Z will also be the winner under honest score or honest medians.

In a median system with sufficient resolution, Y voters know that, if all
other votes are held constant, any vote they might consider for Z falls
into one of six classes:
-group γ: Y is winning anyway, so there is no need to consider strategy.
-group 0: Bottom rank. This risks electing X if the Z voters are similarly
uncooperative.
-group 1: Below the medians of both Y and Z, but above bottom rank.
Strategy could not help elect Y. The only effect it could have would be to
encourage voters in future elections to be more strategic. That would be
more likely to favor X, and almost as likely to favor Z, as it would be to
favor Y; so on the whole, strategy is NOT in the Y voters interests in
either short or long term.
-group 2: Below the median of Z but above that of Y. In this case, strategy
would not help directly, but it could be seen as opening up "strategic
room" for the voter(s) in group 3 to swing the election. Still, the same
considerations as group 2 apply, and so strategy is not favored on the
whole.
-group 3, "pivotal": At Z's median. In the limit of infinite precision
votes, this will only be true for one voter. For this voter, *if* group 2
is empty due to strategy, then strategizing will be strategically favored
until they reach the second-bottom rating, or below Y's median, whichever
is higher. If group 2 is not empty, though, strategy will not be favored,
except perhapes expressively; dropping their vote to the next lowest Z
rating will shrink Z's margin of victory.
-group 4: Above Z's median: Such a voter could in theory gain a strategic
advantage by leapfrogging below the median vote. However, the fact that
they are considering a vote above the median means that, compared to group
3, their strategic advantage is less and the strategic risk of going to
bottom-rating is greater.

In my initial post in this thread, I perhaps did not emphasize clearly
enough that voters will NOT know which class their honest vote would fall
into. But they do know that logically it must fall into one of the above
classes. The voters who have the most intrinsic motivation to use strategy
will be very same ones who will also know that they are most likely to fall
into groups γ, 1, and 2 -- which happen to be the ones which gain no
advantage whatsoever from strategy. The voters with the least motivation to
be strategic will know that they most likely fall into group 3, for whom
subcritical strategy (dropping to second-to-bottom rating) is unlikely to
work (unless group 2 has all chosen strategy) and extreme strategy
(dropping to bottom-rating) is most dangerous (with the lowest benefits and
the highest risks). And in general, all voters will know that they are very
unlikely to happen to be the one pivotal voter in group 3.

Now, clearly a given Y voter will not necessarily know which of those
classes their honest Z vote would fall into. But the strategic situation is
significantly different from Score (and approval) in two key aspects:

-difference 1: Those with the most to gain and the least to lose from
strategy (groups 1 and 2) are the least likely to have it have any effect.
Therefore, it is significantly more plausible that these voters will vote
honestly; and in that case, such honesty will almost certainly cascade to
the less-strategically-motivated voters in groups 3 and 4.
Another way of putting this same advantage is: while in Score, if the
honest margins are slim, the most-strategically-motivated voters can cause
a pathological win by X, in median systems, it takes participation from
some of the less-strategically-motivated.
-difference 2: There is a "subcritical" strategy option which, as long as
it is used by a minority of voters, is just as powerful as extreme
strategy; but which, in all cases, is safe against a pathological result.

Note that difference 1 is likely to keep more voters honest, and that
reinforces the likelihood that difference 2 will apply: a majority of
voters will be honest, and so subcritical strategy will be just as
effective and far safer.

Note also that subcritical strategy is less likely to spur a vicious cycle
of spiteful retaliation. Many experiments show that humans have a far
greater tendency for such spiteful retaliation than pure short-term
rationality would dictate; various models explain this in terms of
evolutionarily-favored meta-rationality. But I expect that subcritical
strategy will be seen more as "minimal cooperation" than as backstabbing,
and so will prompt less retaliation.

Is any of this getting clearer?

So, to respond to Warren specifically:


2013/6/2 Warren D. Smith (CRV cofounder, http://RangeVoting.org) <
warren.wds at gmail.com>

> Seems to me, much (all?) strategic voting  is done by people who are not
> thinking "I will perform this
> strategy and the other voters will do nothing" but more like  "a zillion
> voters like me will perform strategy along with me plus there will be many
> other counter-strategizing voters."
>

For voters who expect to be in groups 1 or 2, that doesn't change the
situation. I agree that such thinking would apply to groups 3 and 4; but I
think at least part of group 4 would not have enough in common with group 3
to sympathize with them.

>
> In such a situation, notions of the the (one) "pivotal voter" become
> pretty irrelevant.
>
> Also, in the event there is (with a median-based rating method) "1-sided
> strategy" then what happens is, the first strategizer moves the median,
> then the subsequent voters move it more, etc.   As a result of that synergy
> the 456552th strategizer is motivated to exaggerate in his vote even
> though, say, if he had
> been the only one, then there would have been zero such motivation.
>

But the first strategizer is in group 1, and doesn't move the median. It's
not until you run through all of groups 1 and 2 that this feedback begins.
That builds a firewall against strategic feedback.


>
> >What does that mean for the strategic dynamics of the chicken dilemma? It
>> means that, in a very real >sense, those two pivotal voters are the only
>> ones under "strategic pressure".
>>
>
> --so, that quote strikes me as absurdly far away from and irrelevant to
> the real world.
>

Fair enough; that was poorly expressed.

Jameson

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