TLDR: Decisions can be logically correlated with others’ choices, amplifying their impact beyond isolated actions. Utopia embraces FDT.
Prerequisites: None
Male betta fish (a.k.a. Siamese fighting fish) are known for being intensely territorial; if two meet in the wild they often fight to the death. When one of these fish encounters a mirror (or even the edge of their tank) they’ll often attack their reflection, sometimes even seriously hurting themselves by bashing against the glass. Good thing we’re smarter than fish and never make such embarrassing mistakes!
Anyway, let’s talk about the election.
As of writing, the United States is having a big election for (among other things) who will be president. And if you, like me, are a voter in the USA, you may be asking yourself: does my vote matter?
Even focusing on swing state voters, no US presidential election has ever been decided by a single vote. In 1876, the election was decided by a single electoral college vote, but that electoral college outcome was determined by thousands of individual votes across multiple disputed states, not by any single voter’s ballot. The closest a single, typical voter has come to affecting the outcome of a presidential election was probably in 2000, when George W. Bush only won the swing state of Florida by 537 votes. But even then, any one person (or even any 500 people all working together!) couldn't have changed things by making a different decision.
When faced with this kind of analysis, the prospect of voting seems pointless.1 But I think this story doesn’t hold up to philosophical scrutiny. Those who feel their vote doesn’t matter are making a similar error to that of the betta fish that attacks its own reflection.
Playing With Yourself
Let’s imagine a simple game for two players where the goal is to get as many points as possible (how many points the other player gets is irrelevant). Each player closes their eyes and holds out their hand as either a fist or an open palm. Then eyes are opened and each player making a Fist earns one point; each player making an open Palm earns two points for the other player.2
The conventional advice given by game theorists is to always play Fist. Regardless of what the other player does, playing Fist gives more points, making it a “dominant strategy.”
But what if you’re sitting in front of the mirror and the “other player” is your reflection? Playing Fist seems pretty dumb, then, since you can earn more points by having your reflection play Palm. The property that makes the game theory math not apply to the mirror game is that we don’t get to simply assume your reflection’s play is independent from yours. Because the reflection’s action is correlated, you cease being able to only consider how your action influences the outcome—you must also ask how your action influences the other player’s action.
Many people may feel that when standing in front of a mirror this stops being an instance of a game with “two players.” That’s a fair point, but I would counter by saying that we then need to be careful not to assume there are actually two players in a game, just because it naively looks like there are two people playing. It would be very embarrassing to, like a betta fish, treat our reflection as an unpredictable “other” rather than a different perspective on the same being.
For instance, imagine that instead of a mirror, there’s a fancy robot with predictive artificial intelligence that’s trying to anticipate your action and play exactly as you would. Does this machine count as a different player, or is it just a reflection of yourself? If its anticipation is perfect, it will behave exactly like the mirror would, and I think it makes sense to treat it as a reflection. But what if the robot isn’t perfect at guessing? At the other limit—total incompetence and ignorance—the machine clearly isn’t your reflection, and you should play Fist to get the most points. The only sensible way to interpolate smoothly between these two extremes is to conclude that there is a numeric degree of correlation which tracks how much you should think of the other player as a reflection of yourself.
Multiple Perspectives
Are your reflections “you”? I think this is probably a wrong question. You are visible in the mirror, you are visible in the flesh, and you are visible in the robot’s anticipation. We can’t make you less hungry by feeding the mirror, so in that sense the reflection certainly isn’t you, but it’s also foolish to say that examining the reflection tells you nothing about yourself or that you can’t control what the reflection does.
Most people, when thinking about mirrors, take on a the (reasonable!) perspective that their reflection “isn’t them,” but rather that they’re directly causing their reflection to be a certain way, hence the correlation. This is a fine perspective in the case that’s literally about mirrors (indeed, normal adult humans handle mirrors just fine), but people start to get tripped up when thinking about things like the mimic robot, in part because the timing of cause-and-effect is different. With the robot mimic, it may have locked in a guess before you’ve even closed your eyes. “Whatever guess it locked in, I get more points by playing Fist,” thinks the fool as they open their eyes to see the robot also played Fist.
In my essay on determinism I offer a different narrative: that you, in the present, can sometimes make decisions that determine3 how things were in the past. This is merely one way of thinking about things, and I don’t claim it’s the best or only way, but it at least nullifies the embarrassing result of what is, essentially, growling at your own reflection.
Another, perhaps worse, perspective (that I used to use!) is to first observe that you can never be totally sure you’re not in a simulation like The Matrix. Perhaps the mimic robot is anticipating your action by mentally simulating a copy of your that’s trying to predict your behavior! Sure, it seems like you’re not a simulation, but that’s just what the simulator wants you to think. Thus, when you find yourself playing the game against the mimic, you become “indexically uncertain” about whether you’re in the real world or not. This perspective says: “If the mimic simulates people exactly once in order to figure out how they play, there's a 50% chance that I’m in its simulation. Therefore playing Fist has an expected value of 0.5 points (+1 point in the 50% where I’m real), while playing Palm has an expected value of 1.0 points (+2 points for my real self in the 50% where I’m the simulation and thus controlling the robot). Therefore I should play Palm.”
This perspective has the virtue of avoiding the growling-at-reflection behavior, but at the cost of spawning all kinds of weird distractions. Perhaps, after believing that there’s a 50% chance that you’re a short-lived simulacrum you should fall on your knees and beg your robotic simulator to give you at least a few more minutes of precious, precious life?? Perhaps you should attack the evil machine for the mind-crime of simulating you in an agonized state of knowing there’s a high likelihood your existence is about to end?? What if it’s simulating you millions of times?? Is it possible to perfectly anticipate someone without simulating them?? (Would that then mean you should growl at your reflection play Fist against the mimic??) These thoughts become increasingly ridiculous the more the machine resembles a literal mirror. Surely it would be crazy to say there’s a 50% chance of “being inside the mirror world instead of in the real world.”
My preferred stance is to deny the story that I’m choosing my action, and instead take the perspective that I’m choosing (parts of) my policy. A policy is a way to determine what action to take in any particular context (where “context” includes stuff like sensation, memory, and what I happen to be in the midst of thinking about). The behavior of my reflection, my body, and the mimic are all downstream of my policy. In choosing a policy I am not only locking in the local, immediate action of my body, but also of all other instances of that policy, whether they be rich, prefect simulations or low-complexity, imperfect models.
I can be wrong, when I’m playing the game, about the degree to which the other player’s action is correlated with my policy—whether those eyes are my own reflection or a different person—but if that other player is using my policy in some way, I am logically controlling their behavior to some extent, as well as my own. There is no way to have my reflection play Palm while I make a Fist.
Distinct People
I’ve been deliberately holding back in this essay from talking about other human beings, instead focusing on reflections or hypothetical mimic-robots. But the real value in this line of thinking is noticing that other people can be running (a lossy approximation of) your policy, and you’re just as capable of influencing those people through setting your policy as you’d be able to influence a robot or whatever.
I think the easiest version of this to spot is in past and future instances of yourself. If you see a nice slice of cake, you aren’t merely deciding whether to eat that slice of cake, but also whether you are the sort of person who eats cake in these sorts of situations, including potentially many times in the future. It might seem like you can “make an exception just this once,” but unless the process that leads to your action is genuinely4 operating in an exceptional context, you’re really just fooling yourself. Only new information (such as having recently learned about decision theory! or being particularly aware of being stuck in a bad habit!) can reliably break one out of a bad pattern of action because in a very serious sense, only one decision ever gets made for that context, and then it’s set in stone. The first time you act in a fresh context is the most important.5
But just as me-in-2024 is deeply correlated with me-in-2025, my decisions are correlated with yours. We’re used to thinking of the people we meet when we’re not looking into literal mirrors as “other,” and in most respects this makes sense, but there’s also a way in which I am a reflection of you and you are a reflection of me such that it doesn’t make sense to think of our decisions as independent. If we are similar people, we are making the same decision, and thus insofar as we say that decision is “yours,” you get to decide how I behave. In such cases, playing Fist is self-defeating.
It’s easy for these kinds of ideas to spill into religion. Christians have the golden rule. Buddhists have anatta. Hindus have karma. And these are just the obvious, surface-level instances. Indeed, much (most?) religious wisdom is deeply linked with this logic. But I also think there’s a kind of really basic, mundane truth to this. We don’t have to be spooky or mystical to notice that certain groups or demographics can act together, even without literally coordinating or making deals. You are in some of those groups!
When we think about groups of other people, we often sensibly see them as moving together. If a politician says they want to lower taxes or increase farm subsidies, it works pretty well to imagine different groups of people responding to those promises, rather than treating them as uncorrelated individuals. And yet, when reflecting on ourselves we often neglect the group decision that we’re making.
Each election cycle many groups of potential voters talk themselves out of voting because they believe themselves to be powerless individuals instead of a group of people. Many of these groups, I believe, are big enough to change the outcome of a big race, if they woke up to the reality of being a group.
Utopian Decision Theory
The ideas I’ve outlined here are the foundations of a branch of mathematics often called Functional Decision Theory (FDT). Alas, in our world, FDT is largely unknown outside of the Rationality community; mainstream mathematicians and philosophers mostly rely on Game Theory and other decision theories which only really work if we assume that nobody’s decision depends on their knowledge of how other agents/players are likely to behave. And unfortunately, the fact that this line of reasoning is fairly neglected in academia means that FDT still contains many open problems, and to my knowledge, has yet to be formalized in a way that’s not obviously flawed.
Things are perhaps different in Utopia. At the very least we can imagine these sorts of ideas being presented outside of the context of religion and in a way that helps shape a better narrative to why voting is important than vague admonishments like “it’s your duty” and sketchy reasoning about altruistic long-odds lotteries.6
Philosophical ideas may not have the concreteness of technologies or laws, but they serve as the bedrock for a good life. The ability to see one’s self reflected in the eyes of others is a pillar of trust, cooperation, and peace. Utopia prioritizes conversations, debates, and study of such ideas in an effort to help its citizens converge to a place of mutual understanding and appreciation, even if it’s imperfect. Ideas like FDT pave the way to deeper appreciation of reality and the enlightenment that comes with it.
Things are less over-determined in smaller, more local elections, but even in these the odds of being the tiebreaker vote are minuscule (but not zero!). Futarchy doesn’t have this problem, since people’s “votes” are actually weights on what the government should optimize, meaning each person’s voice has a marginal impact on priorities.
Savvy readers may notice that this is The Prisoner’s Dilemma. I like this version because it has a positive-sum framing where it makes sense to play the game as much as possible with everyone you meet (if you like accumulating total points). Yes, they’re equivalent, but our intuitions on these things matter, and thus the choice of zero also matters.
Are you “causing” things to be different in the past? I, personally, reserve the word “cause” for V-structured logical relationships, which almost always point from past-to-future, and use “determine” for the more general relationship of whether certain variables force other variables in the same system to be a specific way.
There’s almost always something that can be used to claim “this is an exception.” But a lot of the time this is an act of self-deception. Knowing the difference between an exceptional situation and a merely specific situation is a difficult art.
We are only imperfect approximations of ourselves from one moment to the next. We behave somewhat randomly. My choices on Monday are rarely totally predictive of my decisions on Tuesday, even if I have the same information. People often under-appreciate the degree to which they’re deterministic, but indeed sometimes one can randomly snap out of a habit or pattern of behavior. These random breaks are exceptional circumstances, and are thus vital for seizing control again and shifting overall behavior. But in general I find it more effective to avoid relying on these accidents and instead treat myself as though I’m perfectly consistent throughout all time.
I’m not disputing that it can be a useful framing to see voting as akin to a lottery where most of the winnings go to strangers. Rather, I think that these arguments often pretend like your decision only impacts your vote, and ignores the correlation we’d see in a better decision theory. A good test is whether the logic of whether to vote changes if we imagine the voting population being much larger or much smaller (while still having the same demographics). From the naive lottery perspective it becomes less valuable to vote if there are many people, while the FDT perspective says that it doesn’t matter, since the size of your coalition also grows.