On 6.8.2011, at 19.40, Jameson Quinn wrote: > 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 related > scenarios that could strategically be made to masquerade as these; 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 to > use their delegated votes. > > 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?
Remember trees :-). In a tree where B and C form one branch they and their voters are bound to support each others. Juho > > JQ > > 2011/8/5 Jameson Quinn <jameson.qu...@gmail.com> > > > 2011/8/5 <fsimm...@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. > > > To review for other readers, we're talking about the scenario > > 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 need the > votes). > > 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 > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info
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