5 general voting pathologies: lesser names of Moloch

Ear­lier, I wrote a primer on vot­ing the­ory. Among the things I dis­cussed were 5 types of patholo­gies suffered by differ­ent sin­gle-win­ner vot­ing meth­ods. I pre­sented these as 5 se­quen­tial hur­dles for vot­ing method de­sign. That is, since they are in what I view as de­creas­ing im­por­tance and in­creas­ing difficulty, you should check your vot­ing method against each hur­dle in or­der, and stop as soon as it fails to pass.

Then I read Eliezer’s book on Inad­e­quate Equil­ibria, and Scott’s “Med­i­ta­tions on Moloch”. They ar­gue that the point of civ­i­liza­tion is to provide mechanisms to get out of per­ni­cious equil­ibria, and the kak­istotropic ten­den­cies of civ­i­liza­tion they char­ac­ter­ize as “Moloch” are ba­si­cally cases where per­ni­cious in­cen­tives re­in­force each other. I re­al­ized that the sim­ple two-player games such as Pri­son­ers’ Dilemma that serve as in­tu­ition pumps for game the­ory lack some of the char­ac­ter­is­tics of my 5 vot­ing patholo­gies. So I want to go back and ex­plain those patholo­gies more care­fully, to help build up in­tu­ition about how multi-player, sin­gle-out­come games differ from two-player ones.

A key point here is that I’m talk­ing about sin­gle-win­ner vot­ing meth­ods; that is, “games” where the num­ber of pos­si­ble out­comes is far less than the num­ber of play­ers. In this case, it’s not a mat­ter of seek­ing an in­di­vi­d­ual ad­van­tage for your­self; the only way for you to win is for your en­tire fac­tion to win equally. This means that I will not be talk­ing about the old­est and deep­est name of Moloch, which is Malthus. All the Molochs in this es­say can and should be kil­led or (mostly) tamed.

Also note that this es­say is not the one I’d write if I were only try­ing to re­cruit the ra­tio­nal­ist com­mu­nity to be­come elec­toral re­form ac­tivists. As an ac­tivist, I think that the most im­por­tant and short-term-vi­able elec­toral re­forms are in the multi-win­ner space: solv­ing the prob­lem of co­or­di­nat­ing pub­lic goods not di­rectly through mechanism de­sign, but in­di­rectly through a com­bi­na­tion of mechanism de­sign and rep­re­sen­ta­tion. Some of my rea­sons for think­ing that are con­tin­gent and have no place here. The one that’s not: I think that the prob­lem of “ain’t no­body got time for all that poli­tics” is worse than the prin­ci­pal-agent prob­lem of a well-de­signed rep­re­sen­ta­tive mechanism. Re­gard­less, I think that this com­mu­nity would rather hear first about these names for Moloch.

In or­der, my patholo­gies — hur­dles for multi-agent shared-out­come mechanism de­sign — are:

Dark Horse

Let’s say that you have a 3-can­di­date elec­tion us­ing the Borda count, and your elec­torate has the fol­low­ing true util­ities:

49: A9.0 B1.0 D0.0

48: A1.0 B9.0 D0.0

3: A1.0 B0.0 D9.0

Un­der the Borda count, each voter must give the three can­di­dates 2, 1, and 0 points in some or­der. If the B vot­ers strate­gize, the elec­tion might look like:

49: A2 B1 D0

48: A0 B2 D1

3: A1 B0 D2

B wins with a to­tal of 145. The A vot­ers might try to re­tal­i­ate with a similar strat­egy:

49: A2 B0 D1

48: A0 B2 D1

3: A1 B0 D2

But now D wins with a to­tal of 103, even though D was hon­est last prefer­ence for 97% of vot­ers.

This “Dark Horse 2” ex­am­ple be­comes even harder to re­solve if you make it “Dark Horse 3″:

34: A9.0 B2.0 C1.0 D0.0

33: A2.0 B9.0 C1.0 D0.0

33: A2.0 B1.0 C9.0 D0.0

I’ll let you work it out for your­self, but the up­shot is that each group has an in­cen­tive to give D the sec­ond-most points; that if one or two groups are strate­gic, they can profit; but if all three are strate­gic, all of them lose. D can win in this situ­a­tion with liter­ally zero hon­est sup­port — an epi­cally patholog­i­cal re­sult.

What does it feel like in this situ­a­tion:

To win hon­estly? “All is right with the world.”

To weakly-lose when ev­ery­one’s hon­est? “I am slightly tempted to strate­gize.”

To weakly-lose when the op­po­nents are strate­gic? “I need to stop be­ing a sucker, and counter-strate­gize.”

To win strate­gi­cally? “I feel a lit­tle bit guilty, but at least I won.”

To strongly-lose strate­gi­cally? “WTF? This sys­tem sucks. If pos­si­ble, I should change it. If not, maybe I should learn my les­son and not strate­gize. But re­gard­less, those other evil sneaky strate­giz­ers against me MUST learn theirs.”

This is the clos­est to a stan­dard pris­on­ers dilemma of all of the vot­ing patholo­gies. As with the stan­dard pris­on­ers dilemma, “so­cial glue” (that is, heuris­tics de­vel­oped through suc­cess­ful co­op­er­a­tion in iter­ated sce­nar­ios) can gen­er­ally avoid break­down. But it’s also the eas­iest to avoid us­ing mechanism de­sign: just don’t use the Borda count (or any other strictly-ranked point-based method). That is to say, don’t force peo­ple to dishon­estly sup­port D in merely in or­der to op­pose some other can­di­date.

So “Dark Horse” is a name for a Moloch that’s out­stand­ingly evil but not par­tic­u­larly pow­er­ful.

Lesser evil

If you live in the US, UK, Canada, or In­dia — or any other coun­try that uses First Past the Post vot­ing — you already know this Moloch well. In a sys­tem where you can only vote for one, you’d bet­ter not “waste your vote” on the op­tion you most truly sup­port; you must in­stead sup­port the lesser evil, the least-bad of the vi­able op­tions. The log­i­cal end-point is a world with only two op­tions, each of which has far stronger in­cen­tives to make the other side look bad than to ac­tu­ally pur­sue the com­mon good. If you’re lucky, one or both of those two op­tions will pur­sue the com­mon good for the fun of it; if you’re un­lucky, they’ll each be as cor­rupt as they can get away with with­out los­ing sup­port to the other side; but ei­ther way, there’s rel­a­tively lit­tle you can do about it.

Of course, I should point out that this game the­ory doesn’t always play out ex­actly in real life. The US has only 2 par­ties that mat­ter, but most other FPTP coun­tries have a bit more than that, even if the top two mat­ter more than they should. So if you want to con­tinue to spar with the teeth of this Moloch in­stead of just cut­ting off its head, OK, you’re not doomed to lose ev­ery time. Just most of the time.

In terms of elec­tion sce­nar­ios, this looks some­thing like the fol­low­ing. Utilities are:

15: A9.0, B8.0, C0.0

36: A8.0, B9.0, C0.0

24: A0.0, B9.0, C8.0

25: A0.0, B1.0, C9.0

Votes are:

15+36=51: A

24+25=49: C

This is an equil­ibrium be­cause, in most games where there are far more play­ers than out­comes, al­most ev­ery­thing is an equil­ibrium; no one voter could get a bet­ter out­come by chang­ing their vote, even though the so­ciety as a whole would be far hap­pier if they could elect B. Any A voter who moved to B would be helping C win; any C voter who moved to B would be mak­ing it eas­ier for A to win, even if next elec­tion hon­est C>A vot­ers are a ma­jor­ity.

I prob­a­bly don’t have to tell you what this one feels like, but here goes any­way:

On top of the win­ning coal­i­tion (15 A vot­ers): “All is right with the world.”

On the bot­tom of the win­ning coal­i­tion (36 B>A>C vot­ers): Con­flicted. On the one hand, “the lesser evil is still evil”. On the other hand, “a vote for B is a vote for C”. Both are true; this dilemma is in­escapable with­out chang­ing the vot­ing method. Short-term in­cen­tives fa­vor con­tin­u­ing to vote for A, and in fact ac­tively sup­press­ing dis­cus­sion of A’s flaws and B’s ideas; but hu­man na­ture fa­vors get­ting mad at A and ex­ag­ger­at­ing their flaws. Either way, mind-kil­ling is likely.

On the bot­tom of the los­ing coal­i­tion (24 B>C>A vot­ers): En­raged. Ripe for a dem­a­gogue.

On the top of the los­ing coal­i­tion (25 C vot­ers): Must… try… harder. Next time, we’ll win!

This is a lesser Moloch, in that we could eas­ily kill it by chang­ing the vot­ing method. Note that pro­por­tional rep­re­sen­ta­tion can (if it’s done well) be just as good at kil­ling this Moloch as the sin­gle-win­ner meth­ods dis­cussed be­low! But it’s still strong enough to rule over most of you who are read­ing these words.

Cen­ter Squeeze

OK, you say; if the Lesser Evil is en­abled by the ex­is­tence of wasted votes, let’s fix that by mov­ing all the votes un­til they’re not wasted. You’ve just in­vented In­stant Runoff Vot­ing (IRV). Each voter ranks the can­di­dates; votes are piled up by which can­di­date they rank first; and then, iter­a­tively, the small­est pile is elimi­nated and those votes are moved to whichever re­main­ing pile they rank high­est (if any). You can stop as soon as one pile has a ma­jor­ity of re­main­ing votes, be­cause that pile is guaran­teed to win.

This would solve the spoiler prob­lem of the 2000 Florida pres­i­den­tial elec­tion. Here’s a sim­plified ver­sion of util­ities in that sce­nario (B/​G/​N stand of course for Bush/​Gore/​Nader):

490: B9.0 G1.0 N0.0 (Bush>Gore)

100: B1.0 G9.0 N0.0 (Gore>Bush)

389: B0.0 G9.0 N1.0 (Gore>Nader)

10: B0.0 G1.0 N9.0 (Nader>Gore)

6: B0.0 G0.0 N9.0 (Nader>no­body)

5: B1.0 G0.0 N9.0 (Nader>Bush)

Un­der FPTP, hon­est vot­ing would “spoil” the elec­tion and let Bush win. But un­der IRV, the Nader sup­port­ers can vote hon­estly; when Nader is elimi­nated, those votes will trans­fer, so Gore will beat Bush 499 to 495.

But what hap­pens if Nader ap­peals to more vot­ers, and 300 of the Gore>Nader vot­ers shift to Nader>Gore? That would mean that Nader had 321 first-choice sup­port­ers, and Gore only 189. So Gore would be elimi­nated first, 100 of those votes would shift to Bush, and Bush would win! In this sce­nario, the cen­trist Gore was “squeezed” on both sides and pre­ma­turely elimi­nated, even though he could have beaten ei­ther of the oth­ers in a 1-on-1 race.

And the re­sult is that, just like in the real elec­tion, Nader’s sup­port­ers ended up helping cause the elec­tion of Bush, the can­di­date most of them like the least. That spoilage doesn’t hap­pen un­til af­ter Nader passes 25%, but it still hap­pens. And this prob­lem is real; it hap­pened in the Burling­ton 2009 may­oral elec­tion (though in that case, the vot­ers whose hon­esty worked against them were the Repub­li­cans).

Now, Cen­ter Squeeze is a much smaller prob­lem than Lesser Evil. If you have a choice, you’d rather run a race with a minefield be­tween 25% and 50% of the way, than one where the minefield stretches from the be­gin­ning up to 50%. If you’re skil­lful, maybe you can build up enough speed in the first 25% to leap over the minefield. And par­ties that stay un­der 25% can at least get more at­ten­tion than those who are stuck around 0% as in Lesser Evil.

What does this one feel like?

Win, not spoiled: “All is right with the world.”

Small fringe party, vote hon­estly, still mat­ter: “At least I tried.”

Medium fringe party, vote hon­estly, spoil the elec­tion: Dilemma. Some will de­cide to be strate­gic; oth­ers will say “wasn’t my fault. It was the fault of those treach­er­ous cen­trists who ranked the greater evil as their sec­ond choice.”

Cen­trist, lose due to spoilage: “Huh? What hap­pened? We’re the right­ful Con­dorcet win­ners, how can we lose?”

Large fringe party, win due to spoilage on the other side: “Ha! My far-off en­e­mies were so dis­gust­ing that some of my nearby former en­e­mies joined my cause! I de­served that.”

Large fringe party, don’t win: “Hmm… how can I di­vide my en­e­mies?”

This Moloch is a rel­a­tively be­nign one, who acts to pro­tect in­cum­bent win­ners but al­lows dis­sent­ing voices up to a cer­tain point. Liv­ing un­der its reign (as, ar­guably, Aus­tralia now does) in­volves oc­ca­sional craz­i­ness but is mostly OK. Still, it can be kil­led.

Chicken Dilemma

This sce­nario ac­tu­ally ex­ists in two sep­a­rate ver­sions, de­pend­ing on the vot­ing method: slip­pery and non-slip­pery slope. Both share the same un­der­ly­ing voter util­ity sce­nario, with two similar can­di­dates who must team up in or­der to beat a third one:

35: A9.0 B8.0 C0.0 (A>B)

25: A8.0 B9.0 C0.0 (B>A)

40: A0.0 B0.0 C9.0 (C)

For the slip­pery slope ver­sion, let’s as­sume the elec­tion uses ap­proval vot­ing: vot­ers can ap­prove as many can­di­dates as they want, and the most ap­provals wins. If vot­ers ap­prove any can­di­date with a util­ity above 5.0, the bal­lots will be:

35+25=60: AB

40: C

A and B end up in an ex­act tie for first place (as Burr and Jeffer­son did in 1800; thus, the chicken dilemma is some­times called the Burr dilemma). C, the can­di­date whom the ma­jor­ity op­poses, has been safely defeated; but the out­come be­tween A and B is es­sen­tially ran­dom. In­cen­tives are clearly high for the first two groups of vot­ers to ap­prove only their fa­vorite can­di­date. If 1 of the A>B vot­ers votes for only A, then A wins; but then, 2 of the B vot­ers can get B to win by switch­ing to only B; and next 2 more A vot­ers defect; etc. It’s a slip­pery slope un­til over 20 of each group defect, and then C wins, an out­come the ma­jor­ity hates.

In game the­ory terms, this is a “chicken” or “snow­drift” game, with 2 equil­ibria: ei­ther the A vot­ers sta­bly co­op­er­ate and the B vot­ers sta­bly defect, so that B wins, or vice versa. But in emo­tional terms, nei­ther of these equil­ibria feel sta­ble: both are ar­guably “un­fair” cases where one group is ex­ploit­ing the other’s co­op­er­a­tion. It might be “fair” if the smaller group was re­li­ably the one to co­op­er­ate, but that’s hard to co­or­di­nate in prac­tice in cases where the sizes are similar, both sides will prob­a­bly bet that they are the larger group. So in prac­ti­cal terms, prob­a­bly the more “sta­ble” out­comes are “both en­force co­op­er­a­tion, and hope there’s some odd C vot­ers who care enough to swing the elec­tion one way or the other”, or “both bicker and defect”.

To im­prove mat­ters, we can use a non-slip­pery-slope vot­ing method such as 3-2-1 vot­ing. In this method, vot­ers rank each can­di­date “good”, “OK”, or “bad”, and the win­ner is de­cided in 3 steps. First, choose 3 semifi­nal­ists, those with the most “good” rat­ings; then of those, choose 2 fi­nal­ists, those with the fewest “bad” rat­ings; then of those, the win­ner is the one rated higher on more bal­lots (the pair­wise win­ner).

(When choos­ing the third semifi­nal­ist, there are two ad­di­tional rules. First, to avoid a clone-can­di­date in­cen­tive, they must not be from the same party as both of the first two or, in a non­par­ti­san race, do not count their “good” rat­ings on the same bal­lots as also rated the first semifi­nal­ist “good”. Se­cond, to avoid a dark horse is­sue, they must have at least 12 as many “good” rat­ings as the first semifi­nal­ist. If no can­di­date meets these crite­ria, then skip step 2.)

In this method, if each voter votes hon­estly, then all 3 will be semifi­nal­ists (elimi­nat­ing any also-rans whom we left out of the sce­nario for sim­plic­ity); A and B will be fi­nal­ists (elimi­nat­ing the ma­jor­ity loser C); and A will win, as the hon­est pair­wise win­ner be­tween those two.

It’s still pos­si­ble, in this sce­nario, for 21 B vot­ers to defect, rate A as “bad”, and cause B to win. But if un­der 20 of them do so, it doesn’t change the re­sult. Thus, there’s no “slip­pery slope”. Even though “ev­ery­one co­op­er­ates” is not a strong Nash equil­ibrium in strict game the­ory terms, it is prob­a­bly strong enough to en­dure in prac­ti­cal terms.

Is it pos­si­ble to make a vot­ing method with­out even a non-slip­pery chicken dilemma? Yes, we’ve already seen that: IRV. But since defec­tors in the chicken dilemma look ex­actly like fringe vot­ers in cen­ter squeeze, it’s im­pos­si­ble to fully solve the chicken dilemma like this with­out cre­at­ing a cen­ter squeeze prob­lem — one I’d ar­gue is worse, at least as com­pared to the non-slip­pery CD.

What does a non-slip­pery CD feel like? If both sides co­op­er­ate, I’d ar­gue that it feels ba­si­cally fair to ev­ery­one in­volved. If the smaller side wins through strate­gic defec­tion, that feels un­fair, and tech­ni­cally it’s an equil­ibrium; but I’d ar­gue that hu­man stub­born­ness is enough to counter-defect as a pun­ish­ment, and thus iter­ate back to co­op­er­a­tion. 9 So non-slip­pery CD isn’t re­ally Moloch at all. And as for slip­pery CD… it’s mean, but capri­cious, and can some­times be dis­tracted or over­come.

Con­dorcet Cycles

Here’s the sce­nario. In­stead of util­ities, I’ll just give prefer­ences, be­cause there’s al­most no way to make this one “re­al­is­tic”.

34: A>B>C

33: B>C>A

33: C>A>B

This sce­nario is so un­avoid­ably strate­gic that it’s at the heart of a proof of the Gib­bard-Sat­terth­waite the­o­rem that no (non-dic­ta­to­rial) vot­ing method can en­tirely avoid strat­egy. If one of the three groups pre­emp­tively throws their fa­vorite un­der the bus and em­braces their sec­ond choice, the bal­lots will show at least a 66% ma­jor­ity for that sec­ond choice, so any demo­cratic vot­ing method will elect that can­di­date. So to all three groups, this situ­a­tion will feel like a dilemma be­tween rac­ing to sig­nal they’ll com­pro­mise first and most con­vinc­ingly, or hop­ing that the group be­fore them in the cy­cle makes the com­pro­mise.

In prac­tice, Con­dorcet cy­cles prob­a­bly hap­pen only 1-5% of the time. This is true in the most so­phis­ti­cated voter util­ity mod­els I can cre­ate (hi­er­ar­chi­cal “cross­cat” Dirich­let clusters in ide­ol­ogy/​pri­or­ity space), and also in em­piri­cal ev­i­dence (where cycli­cal prefer­ences seem rare but not nonex­is­tent). So this last lesser Moloch is one which can never be defeated, but which spends most of its time in the deep woods and only oc­ca­sion­ally ram­pages out, do­ing sur­pris­ingly lit­tle dam­age in the pro­cess.

Conclusion

I set out to write this be­cause I thought that mul­ti­player game the­ory has some fun­da­men­tal differ­ences from sin­gle-player game the­ory and speci­fi­cally that we need to stop lean­ing so hard on the pris­on­ers’ dilemma. Hav­ing writ­ten it, I re­al­ize that though I touched on these is­sues, I spent most of the time go­ing over more ba­sic points of vot­ing meth­ods. So I’m not sure this es­say is ex­actly what I wanted it to be, but I think what it is can still be at least some­what use­ful; I hope you feel the same way.

I guess my larger point is that evolu­tion has ac­tu­ally equipped us pretty well with so­cial strate­gies for deal­ing with PD or CD, but that by that same to­ken we hu­mans are par­tic­u­larly sub­ject to per­ni­cious equil­ibria of the “lesser evil” va­ri­ety. The feel­ing of “we all agree these aren’t the best op­tions but look­ing for bet­ter ones would waste en­ergy we need to spend fight­ing against the worse one” (lesser evil) seems like at least as im­por­tant a paradigm of Moloch as “if I weren’t evil some­one else would be” (tragedy of the com­mons/​mul­ti­player pris­oner’s dilemma/​dark horse). It’s im­por­tant to re­mind our­selves that mechanism de­sign offers a way out of lesser evil (and thus also cen­ter squeeze); not just in poli­tics, but wher­ever it oc­curs.