Yesterday’s post on counting votes is related to a paradox I’ve been thinking about for a couple weeks. This is a from-memory paraphrase of the description in Martin Gardner’s Aha! Gotcha: Paradoxes to Puzzle and Delight:

Dr. Omega, brain specialist extraordinaire, is conducting a study. First, he scans your brain, has you fill out lots of personality tests, measures the bumps on your head, and looks deeply into your soul. Then he brings out two boxes, one opaque (A) and the other transparent (B). In the transparent box is a $100 bill. He then gives you two choices:

• Choice 1: Take the contents of only the opaque box (box A).
• Choice 2: Take the contents of BOTH box A and box B.

Dr. Omega explains that you that if, based on his tests, he expects that you will take Choice 1, he has placed $1000 in box A. If he expects you will take Choice 2, he has placed nothing in box A.

With that, he leaves for a vacation in Vegas.

Which choice do you take?

Assuming you believe Dr. Omega is good at what he does, I’m pretty sure this is equivalent to the Prisoner’s Dilemma with you playing against your future self.

Here’s the payoff matrix:

		Your Choice
		A	A & B
Omega’s Prediction	A	$1000	$1100
	A & B	$0	$100

Regardless of what prediction Dr. Omega has made, your payoff is always one hundred dollars higher if you take choice #2 (A & B). The only way that can’t be true is if your choice now in some way affects the prediction that Dr. Omega has already made. And yet, if Dr. Omega’s prediction is correct then by choosing A & B you only make $100 rather than $1000 or $1100.

The paradox is even more clear if instead of a brain specialist, Dr. Omega is a time traveler. He jumps a few moments into the future, watches which choice you make, then pops back to the present and sets the boxes as before. If you believe in a single-timeline worldview (it’s already happened, so that’s how it’ll happen, ala The Hitchhiker’s Guide to the Galaxy) then you’re better off choosing A (insomuch as you can “choose” at all in this worldview). If you believe in splitting timelines (you can change the future, ala Terminator) then you’re better off choosing A & B.

I’ve been having an email discussion about the electoral college and whether it makes your vote “count for less” in non-swing states. I think there’s a fallacy in the whole “my vote doesn’t count” argument — it’s like saying “Nadar voters lost the election for Gore” and ignoring the possibility that the millions of people who voted for Bush might have played some small part as well.

To see where you stand on this issue, try this thought experiment:

It’s the day before the election, and 100 people are going to vote in a city council race between Smith and Jones. How much will my vote count?

• A) 1/100th of the deciding power.
• B) Not knowable until the outcome of the election is known.
• C) Depends on whether Diebold machines are used.

It’s the day before the same election, and a fortune teller tells me Smith will win. How much will my vote count if I vote for Smith? If I vote for Jones?

• A) 1/100th of the deciding power.
• B) Depends on whether the fortune teller can also tell me where I lost my car keys.
• C) Depends on whether the fortune teller works for Diebold.

It’s the day after the same election, and 55 people voted for Smith and 45 for Jones. If I voted for Smith, how much did my vote count? If I voted for Jones?

• A) 1/100th of the deciding power regardless of your vote.
• B) Any of the following:
  • B-1) 0% if I voted for Jones, 1/55th if I voted for Smith.
  • B-2) 0% unless I were the 51st person to vote for Smith on election day.
  • B-3) 0% unless my vote was the 51st one to be counted for Smith after the polls close.
• C) Depends on whether Smith knows someone who works for Diebold.

Score:

If you answered mostly A, you’re an empowered, well-balanced citizen who believes in free will.

If you answered mostly B, in your heart you believe in determinism. Stories about time travel and drug-induced insanity upset you, but you’ll attribute it to an over-active basil ganglia.

If you answered mostly C, you’re a well-balanced citizen who believes in free will but realizes that his vote not only doesn’t count, but isn’t even counted.