The evolution of players in the American constitutional game

Another looming threat of Federal government shutdown prompts Timothy B. Lee to concur with the Yglesian view that American constitutional democracy is doomed — or, at least, in need of major structural changes:

The hour-by-hour style of conventional news coverage tends to obscure the big picture: the perpetual crises the US government has suffered over the last decade are a symptom of America’s deeply flawed constitutional system. This isn’t a new insight on my part. You can read Matt Yglesias’s classic 2015 write-up of the argument, which in turn draws on a large body of political science literature.

The basic issue is that the American system of checks and balances was designed for a nation without ideologically polarized parties. . . . The problem is compounded by the fact that it’s so hard to remove a bad president from office.

One seemingly-strong rebuttal to these arguments is that American democracy has survived for a long time, so probably the system is fine. The last Civil War veterans died in the 1950s; unlike most nations on Earth, America has no living citizens with a firsthand memory of existential risk to its constitution. This history of recent stability is probably the main reason that most Americans instinctively reject arguments, no matter how logically sound, that America's constitutional system is fundamentally flawed.

But this rebuttal has less force than it seems. The American constitution is a game, and political actors are players. When people play a game, it takes time to explore the available strategies. Partly this is because, even for relatively simple games, the space of strategies can be immense, requiring time to explore; partly this is because external forces, such as social norms, may prevent players from using optimal strategies initially. However, once a stronger strategy is discovered, it is difficult to stuff the genie back into the bottle; rewards accumulate for those who ruthlessly exploit the most lucrative methods of play, and those who use less optimal strategies are driven out.

A nice illustration of this dynamic can be seen in Google's training of its chess-playing program AlphaZero chess — openings such as the French Defense and Caro-Kann Defense appeared strong to the program while it was training itself, but eventually it abandons these almost entirely in favor of strategies that are inherently stronger, such as the English Opening.

In other words, every nontrivial game is also an optimization process, where the set of players explores the landscape of available strategies over time. In such a process, it is entirely possible for the most prevalent strategies to shift dramatically and even discontinuously; the past is not necessarily a guide to the future.

If you had been taught to play chess by the version of AlphaZero that existed two hours into its training, you might have learned that the French Defense was the "normal" way to win at chess; if I showed you a single later game using the Queens Gambit, you might view that as a temporary aberration. You would be wrong. Likewise, if you came of age in the 20th century, you might view electoral politics as practiced back then as "normal", and the current era, where the government walks up to the brink of shutdown or debt ceiling default every year or two, as a temporary aberration. I suppose it's possible, but the persistence of this observed behavior suggests that it is simply a stronger way for political parties to play the game.

Lee and Yglesias, and the political scientists whose work they draw upon, point to increasing partisan polarization as the cause of the shift in American electoral politics in recent decades. This is fine as far as it goes, but it is important also to realize that the constitutional game itself has always had, encoded within its rules, the possibility of the current configuration of power. The numerous veto points of the American system have always had the potential to be used to hold one policy objective or another hostage. The division of electoral authority between the President and Congress has always had the potential to allow both to dodge accountability for outcomes. It has always been possible for ideologically united parties to gridlock against each other. Accidental features of the American political landscape prevented these strategies from being exploited, but now the players are playing at this level, and thereby evidently beating those who would play differently. There are now only two possible avenues to change: either some novel strategy emerges to beat these strategies, or the rules must be revised.

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Incidentally, this general idea — that a ruleset and the actors who interact with it coevolve — recurs across many fields:

• It is at the heart of the concept of regulatory capture in public choice theory.
• Designers of multiplayer computer games understand that a game's rules must be periodically patched for "balance" as players discover dominant strategies which render the game trivial or un-fun.
• Security researchers are, of course, dreadfully familiar with the fact that every nontrivial system has unknown exploitable vulnerabilities. Once a vulnerability has been found, they would laugh at the notion that you could simply convince attackers not to behave that way, which is the analogue of hoping that American political parties won't use the toxic tactics currently available to them.

You'll find many other places to apply this concept once you have it in your toolkit.

(I've actually been meaning to write a longer essay on this idea and its implications for a while now, but haven't done so for the usual reasons, so this post will have to do for now. Well, this, and my Pinboard tag on the subject)

Centrism begets extremism, in a precise game-theoretic sense

(Excavated from recent unpublished drafts.)

This is not rocket science.

Suppose a couple* is getting divorced and in joint possession of an indivisible good, such as a house. They have agreed that the wife should keep the house, but pay the husband for 50% of the value of the house. Now they get into an argument about the value of the house: the wife will try to claim that the house is worth less, and the husband will claim that the house is worth more. Who will help them resolve this dilemma?

They first take the claim to Carol the Centrist, whose arbitration strategy is "split the difference" because she believes that "whenever two parties disagree, the truth is always somewhere in the middle". Carol will take the average of the wife's estimate and the husband's estimate. Immediately, the wife will claim that the house has value negative infinity, and the husband will claim that the house has value positive infinity. Since the average of negative infinity and positive infinity is undefined in the general case, no agreement will be reached and Carol's arbitration strategy is fucked. Meanwhile, Carol's silly faith in centrism has driven the husband and wife even further apart than they were to begin with.

The husband and wife realize that Carol is a fool, and they take their dispute to Dave the Decider. Dave understands game theory, and therefore he says: "Each of you write your claimed value down on a piece of paper. I will get an independent assessment of the house's value, and just pick whichever of your claims is closest to the assessment." The husband and wife immediately realize that it is in their interest to bid as close to the true value as possible. Given access to the same information, they will simply bid exactly the same price and Dave will not even have to hire his own assessor. He collects a fat arbitrator's fee and goes home. Meanwhile the husband and wife's set of disagreements has been reduced by one.

This is an extremely simple illustration — in fact, literally a textbook illustration — which I learned from my undergrad class with S. J. Brams (previously mentioned). I say all this by way of commenting on M. Yglesias's and H. Hertzberg's posts about a month ago on the wages of "centrism".

What's amusing is that centrists imagine themselves as essentially a moderating influence, when they are exactly the opposite.

This also puts the lie to the claim, which I sometimes hear journalists making, that if you're getting criticism from both the left and the right, you must be doing something right. Journalism that presents "both sides" without taking sides will, in the long term, lead to an objectively less well-informed public, as it creates bad incentives for the actors. As astonishing as it seems, it would be far preferable to attempt to determine the objective truth, and then print verbatim whichever press release is closer to that truth (so long as you announce this strategy beforehand).

Of course, it's not necessary to go to that extreme. One could instead devise a type of journalism which simply says, "A says X, which is close to the truth. B says Y, which is more of a lie compared to X. Here are the details: ..."

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*Given the rest of this post, can you guess the name of the wife and husband?

How Commoners can beat the Mafia (most of the time)

For those who have never played the party game Mafia, here are the rules:

1. An arbiter is selected at random from the players. Call the other players "townspeople".
2. The arbiter uses some random, secret procedure to designate some small fraction (say, 1/4) of the townspeople as Mafia, and the rest as Commoners. One way that works is to take one slip of paper for each player, write down "Mafia" or "Commoner" on each slip, and have players draw from a hat.
3. All the players to close their eyes. Then, at the arbiter's signal, only the Mafiosi open their eyes and look around, so they know the identities of all the other Mafia.
4. The play proceeds in rounds. Each round goes as follows:
   1. First, all the players discuss who might be Mafia, and then vote to execute one person as a Mafioso.
   2. The person who gets the most votes is executed. If there is a tie, the arbiter should flip a coin. The dead player leaves the game, at which point the arbiter informs the town whether that person was a Commoner or a Mafioso.
   3. Dead players tell no tales. Once dead, a player may not communicate with living players for the remainder of the game.
5. Play proceeds until either the entire Mafia is dead, or all the Commoners are dead. The living team wins.

In practice, the Mafia wins as soon as they're a majority, because then they can always outvote the Commoners and execute them all.

What makes this game fun is the social interaction and politicking that goes on when you're deciding whom to execute. The Mafiosi are all trying to influence the voting so that a Commoner gets executed on each round. Meanwhile, the Commoners are trying to detect excessive certainty or bloodlust (which probably indicates a Mafioso --- after all, only Mafia know for certain whom they want executed), so the Mafia can't appear too eager or obvious. It's also a game of teamwork --- a lone clever Commoner can't beat the Mafia unless (s)he can also convince the other suspicious townspeople to trust him/her. A cleverly played game of Mafia will ultimately be won by the Mafia, if they're better actors, or by the Commoners, if they're better at "reading" people. With the right group, this can be lots of fun.

Now I'm going to tell you how to take all the fun out of Mafia. Propose the following strategy to your fellow townspeople:

1. During the first round of discussion, use some mechanism to produce a random ordering of players. One way that works is for everyone to roll a pair of dice, and sort people from highest to lowest roll, rolling again to break ties. Note: if you use this method, you must decide on the exact method for sorting, including whether you're going from low-to-high or high-to-low, before you actually roll the dice.
2. Agree that everyone will vote to eliminate the players in order. Anyone who dissents from this plan must be a Mafioso, and becomes the next target of execution instead of the scheduled player.

Why does this work? Notice the victory conditions: the Commoners win when 100% of the Mafia dies; the Mafia wins when when they outnumber the Commoners. Given that the Commoners have a large majority, most random orderings of the townspeople will list 100% of the Mafia before any point where the remaining Mafia outnumber the remaining Commoners.

Proving this claim formally requires some fairly intense math. I looked at it for a few minutes with one of my friends (who was also a computer scientist). We decided it was hard, and just handwaved our way through it.

(If you're curious, here's the handwaving: on average, over all random sortings, you expect the proportion of Mafia and Commoners in the remaining population to remain roughly constant as the population decreases; so the Mafia will usually not attain a majority. Then, once you get down to a small number of remaining players --- say, N, where 1/N is the fraction of Mafiosi in the original population --- then you expect that, on average, there will be 1 Mafioso left out of those N players. The chance that this Mafioso will be the last one standing is 1/N. Since N > 2, the last Mafioso probably doesn't survive.)

So, on average, over a large number of games, this is a winning strategy for the Commoners. Only Mafiosi would dissent from it; but the really cool thing is that they can't do anything about it, because if they dissent then they reveal that they belong to the Mafia. Even if all of them dissent together, they're outnumbered, so the Commoners will just execute them all. And even if the Mafia win --- as they sometimes will --- the win doesn't give them much satisfaction, since it wasn't through the exercise of wit and deception but just a random roll of the dice.

When you play the game by this strategy --- and I have done it once --- the game goes pretty fast. Everyone votes unanimously to execute the next player on the list. There's no discussion, no politicking, no doubt, and the game becomes a rather grimly fatalistic exercise until the arbiter calls the end. On the other hand, as the person who devised this strategy, I enjoyed watching it play out.

The Commoners won, by the way. Ironically, I was on the Mafia team that time.

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UPDATE 9:30 p.m.: I got curious, so I wrote a Python script to simulate many games of Mafia in aggregate. Basically, the handwaving analysis above is a decent approximation of the actual results for typical party-sized populations (6-30 people) and small fractions of Mafia. At a population of 25% Mafia, the Mafia wins about 25% of the time. As the number of Mafia increases, however, the results begin to diverge from this analysis, due to the asymmetry in winning conditions: the Mafia win at a rate that exceeds their fraction of the population. At about 39% Mafia, the game becomes 50/50 Commoners v. Mafia.

The source for the script follows. It's a pretty direct interpretation; I haven't tried to do any of the obvious optimizations for simulating games.

#!/usr/bin/env python

import random

TRIALS         = 100000
MAFIA_FRACTION = 0.39
MIN_POP        = 6
MAX_POP        = 30
HIT_VARIANT    = 0

COMMONER = 0
MAFIA    = 1

maf_wins = 0
com_wins = 0

def init_town():
    popsize = random.randint(MIN_POP,MAX_POP)
    town = [COMMONER for j in range(0,popsize)]
    maf_count = int(MAFIA_FRACTION * popsize)
    for j in range(maf_count):
        while 1:
            idx = random.randint(0,popsize-1)
            if town[idx] != MAFIA: break
        town[idx] = MAFIA
    return town

def hit_commoner(town):
    if COMMONER not in town:
        return town
    else:
        com = town.index(COMMONER)
        return town[:com] + town[com+1:]

for i in range(TRIALS):
    town = init_town()
    while len(town) > 0:
        town = town[1:]
        if HIT_VARIANT: town = hit_commoner(town)
        maf_left = town.count(MAFIA)
        pop_left = len(town)
        if maf_left > (pop_left/2):
            maf_wins += 1
            break
        elif maf_left == 0:
            com_wins += 1
            break

print "Commoner wins  : " + str(com_wins)
print "Mafia wins     : " + str(maf_wins)
print ("Mafia fraction : " +
       str(float(maf_wins)/float(maf_wins+com_wins)))

UPDATE 1 Sept: In comments, Andrew and AJ reminded me of a variation of the rules, wherein the Mafia get to secretly "hit" one Commoner in each round, after execution. I've fixed the script so that the HIT_VARIANT flag controls whether to play with this variation. The results are surprising --- see comments for details...

C. Shalizi on crowds and algorithms; also further complaints from yours truly

C. Shalizi has many useful things to say, and to link, about "the wisdom of crowds", partly in response to something I posted a while back.

Shalizi includes a pointer to a Rational Herds: Economic Models of Social Learning (ISBN 052153092X). Aside from having really cute penguins on the cover --- reason enough to buy most books --- the book also looks intellectually fascinating, and instantly makes my to-read list, though with my recent binge of book-buying [0] I most likely won't get around to reading it anytime soon.

In related news, I actually read/skimmed large chunks of The Wisdom of Crowds whilst browsing during the aforementioned book-buying binge. I concluded that the book itself (as opposed to the publicity, or the vulgarized versions of Surowiecki's thesis that are making the rounds) is not exactly bad, but rather good, yet frustrating. Surowiecki's tackling an important subject. He writes with the fluency and accessibility you'd expect from a New Yorker writer. The book recounts many fascinating anecdotes, and it even lays out a set of criteria for organizing "wise crowds" that's sensible and convincing (though stated too vaguely for my tastes). But these strengths make the book's failures all the more disappointing. Each chapter contains at least a few things that get my ersatz-scientist hackles up: an overgeneralization from meager data, or an incomplete and vague summary of a more systematic study, or an example cherry-picked to support his point without adequate treatment of counterexamples [1]. The best ideas in Surowiecki's book aren't new, and the intellectual frame he puts around them often adds little [2]. Lastly, and perhaps most importantly, as Shalizi writes in the post linked above, although Surowiecki does give a nod to the difficulties of crowd organization, in general he does not place enough emphasis on it.

My guess, therefore, is that readers genuinely interested in the ideas Surowiecki discusses would be better off reading the primary sources in Surowieki's acknowledgments. I don't have a copy handy, and I regrettably forgot to scribble them down. Oh well. Next time I'm in a bookstore...

Bonus link: Radio National interview with Surowiecki.

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[0] At the Cherry Creek Tattered Cover in Denver, last week, while visiting a friend; the bargain shelves should be labeled with warnings for compulsive verbivores.

[1] For example, one form of "crowd wisdom" that Surowiecki returns to several times is the fact that groups of people appear, in aggregate, to be very good at estimating quantities. One of Surowiecki's stories in support of this claim: in 1906, economist Francis Galton found that crowd of people at a fair were collectively able to estimate the weight of a thousand-pound-plus ox to within one pound, better than any individual in the crowd. He has a few more examples in this vein, but almost no discussion of the abundant counterexamples. For example, experiments show that, on average, people consistently overestimate the height of men and underestimate the height of women, even when they're shown photographs of the subjects standing next to common reference points. Surely a trained surveyor would do much better than a crowd in this case. Surowiecki briefly mentions some studies wherein experimenters were able to skew estimation results by using explicit suggestion, but he ignores systematic, consistent, a priori bias --- which gives the reader the impression that estimation bias is something induced in relatively rare and peculiar circumstances.

[2] Returning to the collective estimation problem in the previous footnote: the success of averaged estimates would lead me to conclude that the human senses can measure accurately, but with a random error that follows a symmetric (Gaussian?) distribution. This is interesting, but it says little about the "wisdom of crowds". Instead, it testifies to the value of repeated measurement, a bog-standard part of scientific orthodoxy. You will get similar results with inanimate scientific instruments (e.g., a thermometer or a light-sensitive CCD) operating near the limits of their precision: measure many times, and you get a better, rounder bell curve than if you measure only a couple of times. Surowiecki's framing seems simply superfluous here.