[EM] Chicken problem (was: SODA and the Condorcet criterion)

Jameson Quinn jameson.quinn at gmail.com
Sat Aug 6 09:40:06 PDT 2011

```More thoughts on the "chicken problem".

Again, in Forest's version, that's a scenario like:

48 A
27 C>B
25 B>C

C is the pairwise champion, but B is motivated to truncate, and C to
retaliate defensively, until A ends up winning.

In my opinion, scenarios like this make the single most intractable
practical strategy problem in voting theory:

- Approval, Range, and median-based systems all suffer directly.
- Most winning-vote-like Condorcet systems fall prey, including
otherwise-great systems like Schulze.
- Margins systems have no truncation incentive - but as a direct
consequence, they give extremely difficult-to-justify results if the B block
truncates; in fact, they allow a strategic C block to fool the system into
thinking it's seeing this scenarion when actually B and C are mortal
enemies.
- IRV does relatively well with this scenario - but in return, pays no
attention at all to the second choice of the A voters, which should be
decisive if it exists.
- At the other extreme, some systems resolve this problem by forcing
strict rankings from the A voters - but if they really don't have a
preference, that ends up being just statistical noise, and doesn't even
necessarily remove the game-of-chicken incentives if things are balanced
right. Moreover, forcing B and C voters into strict rankings only makes them
escalate their truncations into burials.

Most of us, when we want to "test" our voting systems with a difficult case,
use a strict-ranking Condorcet cycle of three; the old, standard ABC BCA CAB
scenario. That's nice and simple, but not very realistic. To me, the "game
of chicken" scenario; the resulting Condorcet cycle if B truncates; and
are better practical tests for a voting system. In fact, I'd go so far as to
guess that *a real-life Condorcet cycle would be more likely to be the
result of playing chicken than of honest preferences.*

As Forest already explained, SODA, as currently formulated, resolves the
game of chicken — if all votes are delegated. It can do that because games
among finite candidates are much more tractable than those among oceans of
voters. SODA's "sequential trick" would be ridiculous with voters; imagine
"Your turn to vote is on Sunday at 2:35:58 PM."

In my previous message in this thread (Re: SODA and the Condorcet
criterion), I pointed out that there's still a problem if voters explicitly
truncate by refusing to delegate. But I've been considering this issue, and
eventually I found a solution that I think is simple enough to include in
SODA:

*Make all candidate's predeclared rankings into strict rankings by breaking
declared ties in order of the current approval totals when it's their turn

So if B voters truncated, candidate A would see that B was headed for a win,
and would have the option to delegate to C. All the truncation would have
accomplished would be to make A into a kingmaker between B and C. Since A
could have had this kingmaker power, if she had wanted it, from the start,
that's not a problem. The only difference between this end-game kingmaker
power of A's, and if she had simply declared a preference from the start, is
that the end-game power could in theory arise no matter which of B or C has
more approvals, whereas an initial preference would only confer kingmaker
power if the preferred candidate ended up with fewer approvals.

Is this version of SODA really the only system to have a fully-satisfactory
resolution to the chicken problem? Even if it is, is it worth adding this
additional complexity to SODA? Can anyone make a chicken-like scenario which
still stumps this SODA version? (If your scenario has more than 4
candidates, please use DAC instead of approval to find the SODA order of
play.) Or do you know of a different system which creatively resolves the
chicken problem?

JQ

2011/8/5 Jameson Quinn <jameson.quinn at gmail.com>

>
>
> 2011/8/5 <fsimmons at pcc.edu>
>
> Jameson,
>>
>> as you say, it seems that SODA will always elect a candidate that beats
>> every other candidate majority
>> pairwise.  If rankings are complete, then all pairwise wins will be by
>> majority.  So at least to the degree
>> that rankings are complete, SODA satisfies the Condorcet Criterion.
>>
>> Also, as I mentioned briefly in my last message under this subject
>> heading, SODA seems to completely
>> demolish the "chicken" problem.
>>
>
> Well.... almost. See below.
>
>
>>
>>
>> 48 A
>> 27 C>B
>> 25 B>C
>>
>> Candidates B and C form a clone set that pairwise beats A, and in fact C
>> is the Condorcet Winner, but
>> under many Condorcet methods, as well as for Range and Approval, there is
>> a large temptation for the
>> 25 B faction to threaten to truncate C, and thereby steal the election
>> from C.  Of course C can counter
>> the threat to truncate B, but then A wins.  So it is a classical game of
>> "chicken."
>>
>> Some methods like IRV cop out by giving the win to A right off the bat, so
>> there is no game of chicken.
>> But is there a way of really facing up to  the problem?  i.e. a way that
>> elects from the majority clone set
>> by somehow diffusing the game of chicken?
>>
>> The problem is that in most methods both factions must decide more or less
>> simultaneously.  However,
>> if the decisions can be made sequentially, then the faction that "plays"
>> first can safely forestall the
>> chicken threat of the other.  That's one reason that it makes sense for
>> SODA to have the candidates
>> play sequentially, and to have the strongest candidate of a clone (or near
>> clone) set go before the other
>> candidate or candidates in the clone set.
>>
>> Since DAC is designed to pick out the strongest candidate in the plurality
>> winner clone set, it is a
>> natural for setting the order of play (in the sophisticated version of
>> SODA).
>>
>> Another way to solve the chicken problem is to not allow truncations.  But
>> in SODA it seems essential
>> to allow the candidates to truncate.  However there is a pressure  for the
>> candidates to not truncate too
>> high up in the rankings; if they do, they lose credibility with their
>> supporters, so fewer of them will
>> delegate their approval decisions to them.
>>
>
> That is a key point. The other aspect of SODA is that it allows candidate A
> to change their rankings after they see candidate B's rankings. In the rules
> on the SODA page, it is deliberately left vague how many recursions of that
> are possible, or what the exact rules are there. One possible rule would be
> some form of binding "I'll prefer you if you'll prefer me" declaration, to
> avoid recursion. The point is that, however the rule works formally, that no
> candidate will ever get caught by surprise, and so any candidate can make a
> credible threat: I'll truncate you if you truncate me.
>
> That is not to say that all inter-candidate preferences would be mutual.
> Just that if both sides agreed that mutual preference was appropriate, as in
> a true case of near-clones, there could be no "sneak attacks" of truncation.
> In other cases, truncation threats between candidates would be almost
> certainly inneffective... "OK, go ahead and truncate me, I don't like you
> anyway.". The candidate making the threat is either weaker (in which case
> they have no reason to make it, because they'll never get the transferred
> votes) or stronger (in which case they have no reason because they'll never
>
> So, I'm satisfied that SODA has enough safeguards against over-truncation
> by candidates, which helps resolve the "chicken problem".
>
> However. SODA still does not completely eliminate this problem. Individual
> voters, by voting explicitly non-delegated bullet votes, still can truncate,
> if they realize it works. That is much less likely, because a "lazy" voter
> will delegate by default. After all, If Fsimmons does not see this strategy
> possibility, how many normal voters will? Still, I must admit, it's
> possible.
>
> I've thought of ways to resolve it, but I don't see any easy, simple ones.
> It is absolutely not an option to keep voters from casting non-delegated
> votes. One possibility is that a candidates second-hand votes (that is,
> votes which were originally delegated to another) are weighted by D/(D+U),
> where D is that candidate's delegated total and U is that candidate's direct
> undelegated approval total. This does a good job at fixing the
> voter-truncation chicken problem - but it makes the system badly
> nonmonotonic. Any candidate who received more second-hand than first-hand
> votes would have their final total reduced for each direct approval they'd
> gotten! So you could fix the fix, ensure so that second-hand votes beyond
> D+U were weighted fully... but by now, you could certainly no longer call
> the system SODA, it would become CODA.
>
> So I think the best thing to do is just ignore this vestigal chicken
> problem.
>
>
>>
>> Since having complete rankings helps both in chicken and with regard to
>> the Condorcet Criterion, it
>> might be worth using the implicit order in the approval ballots of the
>> supporters of candidate X to
>> complete X's rankings by using that implicit order to rank the candidates
>> truncated by X (or otherwise
>> ranked equal by X).
>>
>
> Ugh. The big problem with this is that approval-style votes for a candidate
> will be, by definition, from voters who disagree with that candidate's
> actual ordering. Also, as a small group, it would be very vulnerable to
> hijacking, at little cost.
>
>
>>
>> This would discourage X from too much truncation, and would make it more
>> likely that the true CW was
>> elected in the (usual?) case where there is one.
>>
>
> Yes, I sympathize with the goal. But I can't see how to achieve it without
> inventing CODA.
>
> JQ
>
>
>>
>> Forest
>>
>>
>>
>> > From: Jameson Quinn
>> > To: EM
>> > Subject: [EM] SODA and the Condorcet criterion
>> > Here's the new text on the SODA
>> > page> Delegated_Approval#Criteria_Compliance>relatingto the Condorcet
>> > criterion:
>> > It fails the Condorcet
>> > criterion,
>> > although the majority Condorcet winner over the ranking-
>> > augmented ballots is
>> > the unique strong, subgame-perfect equilibrium winner. That is
>> > to say that,
>> > the method would in fact pass the *majority* Condorcet winner
>> > criterion,assuming the following:
>> >
>> > - *Candidates are honest* in their pre-election rankings.
>> > This could be
>> > because they are innately unwilling to be dishonest, because
>> > they are unable
>> > to calculate a useful dishonest strategy, or, most likely,
>> > because they fear
>> > dishonesty would lose them delegated votes. That is, voters
>> > who disagreed
>> > with the dishonest rankings might vote approval-style instead
>> > of delegating,
>> > and voters who perceived the rankings as dishonest might
>> > thereby value the
>> > candidate less.
>> > - *Candidates are rationally strategic* in assigning their
>> > delegated vote. Since the assignments are sequential, game
>> > theory states that there is
>> > always a subgame-perfect Nash equilibrium, which is always
>> > unique except in
>> > some cases of tied preferences.
>> > - *Voters* are able to use the system to *express all relevant
>> > preferences*. That is to say, all voters fall into one of two
>> > groups: those who agree with their favored candidate's
>> > declared preference order and
>> > thus can fully express that by delegating their vote; or
>> > those who disagree
>> > with their favored candidate's preferences, but are aware of
>> > who the
>> > Condorcet winner is, and are able to use the approval-style
>> > ballot to
>> > express their preference between the CW and all second-place
>> > candidates. "Second place" means the Smith set if the
>> > Condorcet winner were removed from
>> > the election; thus, for this assumption to hold, each voter
>> > must prefer the
>> > CW to all members of this second-place Smith set or vice
>> > versa. That's
>> > obviously always true if there is a single second-place CW.
>> >
>> > The three assumptions above would probably not strictly hold
>> > true in a
>> > real-life election, but they usually would be close enough to
>> > ensure that
>> > the system does elect the CW.
>> >
>> > SODA does even better than this if there are only 3 candidates,
>> > or if the
>> > Condorcet winner goes first in the delegation assignment order,
>> > or if there
>> > are 4 candidates and the CW goes second. In any of those
>> > circumstances,under the assumptions above, it passes the
>> > *Condorcet* criterion, not just
>> > the majority Condorcet criterion. The important difference
>> > between the
>> > Condorcet criterion (beats all others pairwise) and the majority
>> > Condorcetcriterion (beats all others pairwise by a strict
>> > majority) is that the
>> > former is clone-proof while the latter is not. Thus, with few
>> > enough strong
>> > candidates, SODA also passes the independence of clones
>> > criterion
>> > .
>> >
>> > Note that, although the circumstances where SODA passes the Condorcet
>> > criterion are hemmed in by assumptions, when it does pass, it
>> > does so in a
>> > perfectly strategy-proof sense. That is *not* true of any actual
>> > Condorcetsystem (that is, any system which universally passes
>> > the Condorcet
>> > criterion). Therefore, for rationally-strategic voters who
>> > believe that the
>> > above assumptions are likely to hold, *SODA may in fact pass the
>> > Condorcetcriterion more often than a Condorcet system*.
>> ----
>> Election-Methods mailing list - see http://electorama.com/em for list
>> info
>>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20110806/55abfe2c/attachment-0003.htm>
```