As far as making a difference on the outcome of an election (let alone policy) the probability, say, for a Texan voting in the Presidential election of 2024, even by the most generous calculation (which I strongly dispute on many grounds), which I'll call Chamberlain & Rothschild 1980) the probability is far less than for being struck by lighting in any particular year (not your lifetime risk, which is many times higher).
This calculation was the leading one suggested by google and this reference, from which the academic publisher will grudgingly let you view and download the first page. From that first page, we learn that the probability of casting a decisive vote (basically assuming everything else is random) is 1 / N, where N is the number of voters. About 9 million voters voted for President in Texas in 2016, so to keep it to round numbers we'll say 10 million might be expected to vote in 2024. That means that your probability of casting a decisive vote in Texas would be estimated as:
1 / 10,000,000
The probability of being struck by lighting in any one year is about 10 times that, or around 1 in 1,000,000
Are odds like that worth sullying your self respect by voting for a (likely or proven) war monger, etc, because he/she's the lesser of two evils?
I don't think so. They're not worth getting out of bed. What is worth getting out of bed is satisfying your soul. So you might as well just vote your conscience or even your feelings, which will show up in the official results, and suggest to everyone the kinds of things YOU would like to see, and which your votes might be on offer for. Will that change anything? Probably not, but it probably wouldn't anyway, and it could make you feel better, and less dissociated, more connected with your real feelings, which is one of the big things we need to fight for today.
Now I personally believe the Chamberlain & Rothschild 1980 estimate is far too generous in cases where there is are strong pre-existing political alignments. I personally felt the probability of casting a decisive vote in the Presidential election in Texas to be more like 1 in a quadrillion because of the low probability of the Texas of today going to 50% for a Democrat. It's not random, it's strongly aligned to Republicans.
I think any useful look at these things has to include the 'prevailing winds' of existing political biases. So I start from some vote, which could be the vote of 2016 (which didn't follow a pandemic so I think is more representative). Trump won that election by in Texas by about 800,000 votes out of about 9,000,000 votes cast.
Starting from the final outcome (that final outcome, because we don't have the current one) and working back to a tie vote which you would cast the deciding vote on, 800,000 votes would have to change (assuming they come from otherwise non-voters or 3rd party voters). For each change of one vote, it could change backwards or forwards. Requiring it to change in a desired direction therefore happens at about 1/2 the probability of a desire change. (Technically there are vast possibilities either way, but roughly equal either way too.) So, requiring 800,000 votes to change in a desired direction would happen at:
1 / (2 ** 800,000)
Read as 1 over 2 to the 800,000th power.
I can't get anything I have to calculate that number it is so small. Roughly estimating 3 powers of 2 for each 10, it approximates to 1 / (10 ** 300,000), or 1 in 3000 googols.
Now, I'll freely admit, that estimate is too far out. I think the truth is somewhere in between the Chamberlain and Rothschild 1980 estimate and mine. My gut estimate of 1 in a quadrillion still sounds about right to me, given the polarized politics of Texas, etc (and I'd note that it's only a squaring of Chamberlain and Rothschild 1980, which assumes no politics at all). But the best calculation I've come up that includes the pre-existing polarization suggests it's far smaller than even that.
I'm pretty confident I will not be so unlucky as having failed to cast the decisive vote in Texas in 2024, even by the Chamberlain and Rothschild 1980 calculation.
Charles
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