If lotteries could be gamed mathematically, then they would be gamed mathematically, and we'd have a bunch of mathematical millionaires as a result. I'm calling BS on all of this hand-waving. Seriously, how much do you think the miniscule odds of winning can be increased via these methods? I want a numerical answer.
And in any case, these factors do not apply to US Presidential elections and are thus irrelevant to the larger point.
> Seriously, how much do you think the miniscule odds of winning can be increased via these methods?
There are multiple methods that can be and have been used, they all have different outcomes on Expected returns.
> I want a numerical answer.
Again, maybe you might want to work on the math a little yourself - on a specific ruleset (or on a family of rules using some abstraction) .. there are tools that can help you; mathematica, R, etc.
The main issue here is a single vote in a US Presidential election, i.e., one vote out of around 150 million. Thus, the relevant analogy is buying one lottery ticket in a huge lottery such as the Powerball or Mega Millions and matching every number to win the jackpot.
Everything else, including cheating and rigging the lottery, is irrelevant to the question of strategically voting in a US Presidential election. None of your examples or hand-waving have shown that you can significantly improve the odds of one ticket winning the Powerball or Mega Millions jackpot.
> None of your examples or hand-waving have shown that you can significantly improve the odds of one ticket winning the Powerball or Mega Millions jackpot.
No one has said that you can improve the odds of one ticket winning. What has been said is that you can improve your expected value of playing one lottery ticket by carefully choosing what ticket to buy.
Your expected value is the product of:
• The probability that your ticket wins
• The value of the prize
• 1/(N+1) where N is the number of other people whose tickets have the same numbers as your ticket.
The first two factors are the same for everyone. The third depends on the numbers on the ticket because a lot of players do not pick their tickets randomly.
For example 1 2 3 4 5 6 is a surprisingly common choice. I've seen several lotteries where they reported afterwards that if that had been the winning ticket the prize would have been shared by several hundred or even thousands of people.
> What has been said is that you can improve your expected value of playing one lottery ticket by carefully choosing what ticket to buy.
Carefully choosing? AFAICT the so-called strategy is "choose numbers higher than 31". That's a tiny bit helpful perhaps yet still exceeding vague. And this strategy depends on others not also adopting the same strategy, in which case it would actually become counterproductive. If all lottery players acted "rationally", the strategy would cease to exist.
"Thus, the relevant analogy is buying one lottery ticket in a huge lottery such as the Powerball or Mega Millions and matching every number to win the jackpot."
I like your analogy, but I think it needs to account for the fact that there are two scenarios in which a single vote can influence an election:
1. If it would have been a tie without that single vote. In this scenario, the single vote breaks the tie.
2. If the candidate that the single vote is to be cast on would have lost by one vote withtout that single vote. In this case, the single vote creates a tie.
The odds of either happening are astronomically long, of course.
And in any case, these factors do not apply to US Presidential elections and are thus irrelevant to the larger point.