# The Random Number Game

I invented a game, and it goes like this. We’re going to pick a 20 digit number by taking turns choosing each digit. I choose the first digit, then you choose the second digit, I choose the third and so on. Once we’ve chosen all the digits, we use our number as the seed to a random number generator. The random number generator picks a number between 0 and 1, and if the number is greater than 0.5 then I win; if it’s less than 0.5 then you win.

Obviously this isn’t meant to be a “fun” game, it’s more of an open-ended math problem. What’s the strategy? Is there a strategy? Who wins?

The idea behind the random number generator, is that it’s deterministic, and yet opaque. Given any particular seed, the random number generator will consistently pick the same result—either you win, or I do. But there’s no particular pattern to it. It behaves as if the result were randomly chosen. The only way to predict the game’s outcome is to individually plug in each random seed into the random number generator. However, this might be intractable, as there are 10^20 possible seeds.

This game is deterministic, finite, and perfect information—much like Chess. However, it appears that the only real strategy is brute force, by plugging in seeds into the random number generator.

# Capital in board games

In economic strategy board games, it’s very common to have an arc of growth over the course of the game. You start out with few resources, and then you invest those resources to bolster your income, which then gets reinvested to grow even more, following an exponential trajectory. Central to this growth trajectory is the concept of capital.

In economics, capital is understood as durable goods that are used to increase or enable production. The classic example of capital is factory machines, but capital could also be something abstract, such as an education. People commonly understand capital as simply money, which is true insofar as money is commonly invested into capital. And so it is in economic board games, where you invest fictional money into fictional capital in order to increase fictional production.

# Art, success, and rewards

I recently read a story where an artist sold a recording for a flat fee, and then the song went on to become hugely popular, but the artist didn’t receive any royalties. It’s a familiar story of exploitation, especially of Black artists who systematically receive less credit than they are due in American music.

However, I was distracted by an alternative interpretation that came to mind. To some extent, the rights to royalties for a song is essentially a lottery ticket. Song popularity follows a power law distribution (I presume, based on how these things usually work), so that a few songs become extremely successful while the vast majority remain in obscurity. It makes sense to want to sell your lottery ticket–provided that you get a fair price for it. If you have a losing ticket–as most people do–then selling that losing ticket is a way to still make money.

# A 2D voting sim

I made a Monte Carlo voting simulation. No particular reason, I just think it’s neat.

Okay, so I was thinking about the Median Voter Theorem, which says that the winning position in an election is the position of the median voter. Of course, this conclusion only holds under certain assumptions, and none of those assumptions are actually true. And yet the conclusion is approximately correct in many situations. That’s why we care disproportionately about the median congress members (like Susan Collins), the median Supreme Court Justices (like Roberts), and the median “swing” states (like Pennsylvania).

But it should be obvious that the median voter fails in a lot of ways. In particular, it doesn’t predict the political polarization that occurs in US politics. And there are plenty of possible explanations: voter turnout, third parties, primary elections, politician’s charisma factors, multidimensional political spectra, and so on. But I’m not sure which among those explanations are most important.

The voting simulation won’t answer any of these questions, I’m just setting the context. One of the assumptions of the Median Voter Theorem is that political preferences exist along only one dimension. I thought I’d try running simulations with two dimensions to see what would happen, and to make some pretty graphs.

Voters and candidates in a 2D space

# Election meta

cn: more board gaming than election politics, really

Usually around election time I write up a post about what I’m voting for on the ballot. Most things on the ballot are local, and not relevant to most of my readers, but I think it’s important to highlight and normalize the research process for smaller elections. The presidential election is important and all, but in all likelihood you’ve already made that decision so surely you can spare some time to research the smaller elections?

Unfortunately my last ballot didn’t really have any interesting local votes, so I guess we’re stuck talking presidents. Well shoot.

In games with three or more players, players are often presented with a choice to attack one of their opponents. This opens up a fair amount of strategic space, which board gamers sometimes sometimes refer to as “politics”. Common political strategies include:

# Ethics of accuracy

Andreas Avester summarized Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy by Cathy O’Neil. Now, I’m not sure how many readers remember this, but I’m a professional data scientist. Which doesn’t really qualify me as an authority to talk about data science, much less the ethics thereof, but, hey, it’s a thing. I have thoughts.

In my view there are two distinct1 ethical issues with data science: 1) our models might make mistakes, or 2) our models might be too accurate. As I said in Andreas’ comments:

The first problem is obvious, so let me explain the second one. Suppose you found an algorithm that perfectly predicted people’s healthcare expenses, and started using this to price health insurance. Well then, it’s like you might as well not have health insurance, because everyone’s paying the same amount either way. This is “fair” in the sense that everyone’s paying exactly the amount of burden they’re placing on society. But it’s “unfair” in that, the amount of healthcare expenses people have is mostly beyond their control. I think it would be better if our algorithms were actually less accurate, and we just charged everyone the same price–modulo, I don’t know, smoking.

# Intrinsic value of choice

I know that this question has practical and political implications, but for now, I’m treating it as a “just for fun” philosophical question.  Just wanted to be upfront.

What is the value of freedom of choice?  Does it have intrinsic value, or is its value purely instrumental?

A thing has “intrinsic value” if it is valuable in itself.  It has “instrumental value” if it is valuable because it is a means to get something else of value.  For instance, suppose we have a choice between mushroom and cheese pizza.  This choice has instrumental value, because it’s a means for people to have the kind of pizza they most prefer.  But does the choice also have intrinsic value?

Under an initial analysis, I thought the answer was “no”.  If I’m presented with a one-time choice between A and B, and I choose A, did the other option B do any good?  At least within a consequentialist ethical framework, it sure doesn’t seem like it.  After all, option B had no bearing on the consequences.