On Elections & Game Theory & The Real WorldYou should be very skeptical of people who have simple answers to complex problems. They may be right, but for the wrong reasons, and if you adopt those reasons you will be armed with the correct answer but not for long (situations change and what you're relying on won't generalize - that's what it means to be right for the wrong reasons). When people say voting for Candidate X in the 2016 election is simple, it's a no-brainer, only a fool could get it wrong, some of those people are right for the wrong reasons and others are wrong for the wrong reasons (after all, I didn't say which candidate they support), but all of them are wrong for oversimplifying a very complex decision. They are wrong in a way that will produce the wrong answer if applied to a different election, even if they're right in 2016.
The Things the “This is Simple” Folks Likely Aren’t Considering:
Everything is Iterated: Voting and Rationality
Researchers have performed the following experiment, called the ultimatum game, where, for example, researchers give Player A $50 but on one condition: Player A must offer Player B a portion of the $50 (in whole dollar increments), and only if Player B accepts the offered split will either player walk away with any cash. There is a vast literature full of variations, but in the most basic version, it is said that if both Player A and Player B are “rational maximizers” then Player A will offer to give $1 and keep $49. After all, Player B is now faced with a decision between $1 and $0, and thus “should” accept the $1. Accepting $1 is said to be a “dominant” strategy over rejecting and getting $0 – it results in a better outcome every time. Since accepting $1 is dominant, so is offering $1, since that results in the biggest gain ($49) for Player A.
Real life Players A usually offer more than $1 and real life Players B usually don’t accept $1 when offered. These players, despite being easy to find, are ridiculed as “irrational” by some researchers and observers.
In a different variation, the players will do the same exercise twice instead of once, and they know this fact. Playing more than once introduces the concept of an “iterated” game. Even with only 2 events rather than 1, the incentives have changed somewhat. An offer of $1 in Game 1 still gives Player B the choice between $1 and $0, but there is now almost everyone agrees there is a “rational reason” to punish Player A for such a small offer. Player B may establish, as a rational strategy rather than as a “mistake,” a reputation as someone who doesn’t accept offers she perceives as unfair. If these players are to play more than twice, these reputations become increasingly important relative to the $1, or $10, in play in the particular game that is going on.
As with any experiment, the hardest part is figuring out how the results relate back to the real world. Why do most people instinctively feel that rejecting “unfair” offers is a valid strategy that feels better than $1 feels. Why does the supposedly dominant strategy not seem intuitively dominant? Because in the real world, nearly everything is iterated. We live in communities, we have reputations in our communities, and our intuitions seem to have evolved (culturally if not biologically – and results do vary across cultures) to understand that the non-iterated game where your reputation doesn’t matter is the very rare exception, not the rule.
Before we move on, there is one more variation I want to mention. Like I said, the literature is vast, and I am presenting only the tip of the tip of the tip of the iceberg here, the parts that will be relevant later. One thing I learned from the blog Less Wrong is that changing the stakes can change our intuitions. People who reject the $49-$1 split might not reject an offer to split $50 billion $49billion-$1billion, or an offered split of 49 million doses of life-saving medicine to 1 million doses (where a rejected offer means no medicine is manufactured at all) if an evil dictator decides to be Player A. I would say two things are happening here, the first is that these don’t feel like scenarios that are likely to be iterated, and we can pick up on that intuitively. Indeed, if you set up the iterated version even in the thought experiment, the intuitions start to shift (“well, the next offer the dictator will make if I accept this is 1 million more doses or even less, so I can perhaps save more total lives by rejecting – I need to at least consider that.”). Second, the offers feel less “unfair” because the smaller pile is still so significant. This will be important later as the stakes in the real world are often larger than $50.
Note on using Game Theory to “model” real life decisions. Decisions in the real world are complex and most of the important ones won’t have numbers like $49 or $1 attached, and if you try to attach a number, but add disclaimers that the numbers are imprecise, based on certain assumptions that are clearly flimsy, etc., you run a pretty serious risk of trying to make what you’re doing seem more precise than it is. But, I still believe we can model things and learn from the models and even compare outputs, using natural language and intuition. So if I say you can model housing stipends at tech companies as a kind of “arms race” or certain negotiations as a “game of chicken” I am drawing on game theory for a natural language way to express a pattern of decision incentives and constraints, drawing on our intuition and experience in how to navigate them. I don’t mean a model that outputs the correct dollar amount of the ideal housing stipend or the precise place the negotiation should land – those would be different kinds of models.
Presidential Elections – An Iterated Game
If you openly support Gary Johnson or especially Jill Stein, people will politely or not-so-politely inform you that you are making an irrational choice. In fact, a dominated choice. In the case of a progressive who supports Stein, you are told that you can choose to make it slightly less likely that Trump gets elected, or you can choose to have no impact, and thus sucking it up and voting for Hillary is dominant – it accomplishes a small something rather than nothing. Sound familiar?
And as you might expect, I reply that elections are an iterated game. Every four years, we get a new “offer” from the two major parties and a few side players like libertarians and greens.
Our reputation for accepting or declining unfair offers is public, and it does impact the candidates (the offers) we get in future election cycles. In each election cycle, major and minor parties (and the media that covers them) have to decide who they want to hitch their wagon to. And they all have analysts trying to predict who is “electable,” which issues matter, which positions are too risky to add to the platform, and a host of similar choice along the same lines.
Even if these party leaders, media members, and analysts don’t know how Matt Sperling voted last election, they certainly can and will look up how many people voted independent. My vote is counted. Maybe I stay home on election day. They look at turnout, they analyze those numbers. My vote is again counted, though less precisely. The choices that leaders and advisors have to make will be made in a way that tries to “capture” a winning number of votes and they will use past elections to model how people are likely to behave this time. This happens all the time.
Stein and Johnson voters are establishing their reputation in an iterated game. They are declining the unfair offers of Trump or Clinton. Critically, the offer has only gotten this bad because so many people have established a reputation for playing a “non-iterated” strategy of accepting poor offers. If you accept $1 in Game 1 of the iterated version, what is to stop Player A from offering $1 again in Game 2 or an even lower minimum if one is permitted?
The Things I Was Glossing Over Before I Forced Myself to Advocate for Them as an Exercise:
“But Trump is so bad, this feels like a non-iterated game – he might start World War III or appoint a conservative to the Supreme Court for life!” The elephant in the room. The “Trump is so much worse!” argument has a ton of intuitive appeal. Yet my model in the first part of this post hardly considers it. That’s an indicator that I needed to stare at this pretty hard and consider whether my model really shouldn’t just have an input for just how bad the other candidate is. The next exchange (hypothetical as I argue with myself, but you’ll see I surprised myself with which side won the argument!) was instructive:
I forced myself to come up with game theory reasoning for a Hillary vote, to test my reasons against, and then to rebut those rebuttals, etc., here is a summary of the resulting exchange I had with myself (and I didn’t figure this all out by pure introspection but from discussions with others plus introspection, and I present the introspection piece here for review as a clean summary of what I found persuasive on each side):
(“Matt B” - the part of my brain playing Devil’s Advocate): By voting third party based on a model that is agnostic as to how bad Trump is relative to Hillary, you’re not ‘rationally rejecting a low offer’ as you claim, you’re irrationally defecting from a collective strategy of voting along party lines. Political parties are coalitions of voters trying to avoid the collective action problem of 100 people with 100 different sets of preferences all voting for 100 candidates. How exactly to compromise is an incredibly tricky problem, but coalitions of voters that align on at least the big picture issues or big picture approaches to the big issues, is a solution that we’ve landed on with the 2 major parties. When to defect from the coalition becomes thus not simply a question of “is this an iterated game, can I impact future elections with a better vote?” but rather comparing that good to the harm of defecting.
In a winner-take-all election, if one side of the political spectrum forms stronger coalitions of voters than the other side, that side threatens to win every election. Voting along party lines is a cooperative effort to not let the other side win every time by having a stronger coalition.
(Matt A responds): If my coalition is advancing agendas not just slightly misaligned with my values but in direct opposition to them (just to make up some hypotheticals - say the party defrauded its members by supporting one candidate in the “neutral” primary season or the winning candidate in the primary is pretty clearly captured by special interests seeking to perpetuate the status quo under the guise of fake progressivism - again just to make up a hypothetical), then why are you even participating? And intuition about what to do is once again instructive – people in fact stop participating and voter turnout drops in these contexts. You need a line in the sand somewhere for when to defect and not participate in the coalition.
(Matt B): Well, I do have a line for when to leave, the line for when to leave the coalition is when your candidate is worse than the other coalition’s candidate (in which case abandoning has no cost or even has positive effect), or at the very least when the costs of the coalition failing are not so severe that they overshadow the future gains of establishing a reputation for declining unfair offers.
(Matt A): But this level of fealty to the coalitions will lead (and has lead) to a death spiral of two increasingly bad candidates on issues that can be captured by special interests. Your model doesn’t account for getting out of this death spiral. You need a better way out than “their guy is better, cool I'll switch!” as “their guy/gal” will consistently suck from your vantage point - almost by definition of how the coalitions were formed in the first place.
(Matt B): Oh but I do have a way out, since I am a Strongman living in your imagination, I can make my model incorporate yours if I want to. I’m not saying you should always cooperate with the collective effort to stop the other guy. I’m saying you take the output of your model for impacting future election cycles with your reputation (as someone whose vote cannot be captured easily), and compare that to the output of the model that says cooperate no matter what. Cooperation has an expected value, and so does your reputation. You then vote the higher expected value. You formed your model for navigating an iterated election process in defiance of everyone saying the coalition (party) voting model was the whole story, but you went too far. You are right that too often, the party-lines folks are not even engaging with the tradeoff and trying to navigate it. But neither are you. There are two collective action problems here we can effectively think about and informally model, and it is imperative that we model both.
(Matt A): I see what you are saying and it makes sense. This would also allow me to get the relative value of the two candidates into my new model (the combined model) as an input, which makes intuitive sense if you consider that our goal is total utility, i.e. being Game Theory Optimal (actual) not just being Game Theory Optimal (incomplete model). Before, I could feel myself wanting to not have an input in my model for relative strength of the candidates, and thus avoid the "Trump is so awful though" STOP SIGN in some people’s thinking. But I cannot in good faith construct my own equal and opposite STOP SIGN to my own thought process that says “don’t carefully consider what the inputs to your model should be and which inputs feel intuitively wrong to exclude, think first about which inputs will help you win your argument.”
Quick question for you Matt B, what if the coalition leaders used corrupt tactics to bias the coalition electorate, or what if the coalition candidate isn’t all that truthful and you feel others are being tricked, should that matter?
(Matt B): It does matter, as your “should I establish a reputation for not putting up with bullshit” model’s YES output increases as the amount of bullshit increases. It just can’t be the end of the analysis, you still have to compare that output to the costs of defecting from the coalition. You were right that the "I always vote along party lines" people need a line in the sand, but you were wrong about how to draw it.
(Matt A): Okay, I think we have a framework. We better discuss that line and come up with a decision on how to vote this year…
(To be Continued)