Newcomb's paradox

>On the one hand, why bother voting? It's a pain in the ass and my single vote has such a negligible effect. On the other hand, if everyone like me has that same attitude, then I and others like me lose our voice in the election. So should I vote, or not?

There are going to be final poll numbers. Do you prefer that they be an accurate statistical sampling of the population, or a biased one (perhaps biased towards whatever causes some people to vote and others not to)? Your decision on whether to vote, and whether to encourage others to vote, and which others to encourage to vote, is determined by this preference.

There are a couple of simple Nash Equilibria here, as well. Assuming you want your ideology to win the election, you want everyone who agrees with you to vote, and everyone who disagrees with you to stay home. Therefore, you engage in vote suppression against your political enemies and vote recruitment for your political allies. The Equilibria are:

* Negative Nash equilibrium: the piling-up of voter suppression activities of all types causes election outcomes to be determined entirely by who's better at keeping their enemies from voting. Since this is a zero-sum game played against the enemy team's vote recruitment efforts, all teams should notice they've been sucked into a zero-sum, zero-net-productivity black hole, and pass regulations against the worst forms of vote suppression (such as mislabeling polling places or election dates, removing "enemy" demographic groups from the voting rolls, etc.).

* Positive Nash equilibrium: everyone spends lots of effort on vote recruitment efforts, and the actual election outcomes are thus a very accurate statistical sampling of real population preferences.

* Genuinely dangerous and subversive Nash equilibrium: some limited number of political parties consolidate power and trade it back-and-forth, either allowing each-other to win elections or drawing elections laws/boundaries so as to ensure each of them can confidently plan their next round of office-holding. Elections become play-acts of real political contest, and the population's real preferences are increasingly ignored.

You decide which of these we see in different actual democracies right now.

Did you read the article? It answers your question. Take a look at the section that begins with this:

The problem is called a paradox because two analyses that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout. The first analysis argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money.

If you don't find this convincing, that's the point. Half the people who read this think one answer is obviously right, and the other half think the other is obviously right.

In that scenario, the predictor will always "predict" that you will take both boxes.

The lack of information of box B, is exactly what makes the other case different. Then you need to only rely on thinking and you do not know if box B has a million dollars till you open it. If you risk taking two boxes, you will lose it.

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Let me give another example to make the original scenario transparent.

Imagine I will write a function "decide(double content_of_A)" to decide whether B or both will be opened, given content of A.

Imagine you can examine the function beforehand, and you are super-intelligent compared to me, so any attempt to obfuscate the code in my part will be utterly useless and easily seen through.

And you are honest - in putting the $1M in box B if your analysis suggests that the decision function will only take B.

Note that my function gets called after you have placed the money, just as in the original scenario.

Would I not write the function to choose B? I would.

As the sibling/nephew posts indicate, the bet is a good deal for anyone who has faith in The Predictor's ability to predict actions.

We also have a huge range for our bet to cover varying levels of certainty.

Again, this is not win-optimizing, but risk-averting. I am pretty sure I am being generous with the technical definition of risk aversion, but that is not material to my suggestion.

The paradox exists because there is no clear best strategy. The best you can guarantee (without resolving the paradox) is $1000, if you always take A and B you will net at least $1K, with the potential (depending on paradox resolution)for $1.001M. My suggestion aims to increase the guaranteed minimum essentially by purchasing it with the decreased maximum. $500K is really just a Schelling point, but unnecessary.

A bet of $999K is the breakeven point - any bet less than this amount increases your guaranteed minimum such that this guaranteed minimum is always greater than the $1000 which is the guaranteed minimum of taking A and B. Since The Predictor is (depending on version of the paradox) either infallible or nearly so, it seems reasonable to me that you can find someone to take a bet at <$999K.

But I don't think people are wasteful in that sense. Voter participation and voter awareness tends to be low, at least in the USA. Besides, if your government only works if people act in a specific irrational manner, I don't have high hopes for it, especially considering that one usually cited fundamental role of government is to fix problems where individual rationality does not lead to group rationality.

Forcing people to vote doesn't incentivize people to educate themselves on the issues, which is required to "vote responsibly" according to the usual Western civics class description of how democracy is supposed to work.