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Why would the chance of them winning hold any relevance to if i vote for them or not?
@freemo Just reflected on this a bit, open to feedback.
Strictly speaking, it's the chance of casting a decisive vote, not the chance of them winning, that is relevant.
The expected value of voting for a candidate is D*ΔU-C, where D is the chance your vote is decisive, ΔU is the difference in utility (how much better off you'd be under one candidate than another), and C is what it cost you to vote.
D for state and federal races is generally small if you live in a swing state, and infinitesimal otherwise. D for local races may be higher.
Party-line voting is a C-minimising strategy, because it means you hardly need to spend any time researching your choices. Ironically, because D is so low in most cases, this might actually be the "smartest" way to vote (which is kind of depressing, at least to me). Refusing to vote takes this to the extreme and drives C and D both to zero, which is the optimal strategy if you think D*ΔU is less even than the cost of going to vote or mailing a ballot.
Voting third-party maximises ΔU at the expense of D, whereas voting for a major-party candidate maximises D, possibly* at the expense of ΔU. Saying you vote for "the lesser of two evils" is just pointing out that it is the difference in utility ΔU, and not the absolute utility of candidate X U(X), that is used in the formula, which is true. Saying you don't because they're "equally terrible" is equivalent to saying ΔU of the major-party candidates is negligible, which may also be true.
If you live in a state which has a political mechanism for rewarding candidates for votes garnered irrespective of whether they win, or you want to represent intangible benefits like being taken more seriously next election, the easiest way to incorporate this is to reduce C by the marginal utility (to you, not the candidate!) of one vote. Then C is the net cost of casting the vote.
*Some people will just straight-up prefer the major-party candidate to all the third-party options, so their choice maximises both D and ΔU.
@khird I think this misses half the picture. There are two primary effects your vote may have and both need to be considered in tandem..
1) what is the chance of you casting a decisisve vote
2) what effect does it have on future voting if you increase the percentage voted for a third party..
If you vote is not decisive then the effect your vote has is limited to #2.. if you vote primary party then your vote is telling people "hey primary party will always win, third party doesn't stand a chance, don't vote third party"..
So in short when your vote is not decisive you are ultimately voting whether you want to increase the chance of a third party win and higher voter support in the future or not.
Since the chance of your vote being deciscisive is so astronomically unlikely no matter who you vote for we can rule out #1 entirely, it doesn't even matter if your vote stands a slightly higher chance of being decisive for a primary party than a third party because its still so statistically small as to be effectively impossible.
Therefore #2 is the only actual consideration in play... do you wish to perpetuate a two party system and encourage it remain two party into the future, or not.
@freemo I don't think I missed that - it's what I meant by "marginal utility" of a vote in the last full paragraph. But it's highly dependent on your jurisdiction - if your state doesn't have a mechanism where you qualify for easier ballot access in future, or some other direct benefit, then it's basically just bragging rights: "I got six hundred seventy-*three* votes, not six hundred seventy-*two*!" And what's that worth to the candidate - moreover, what's that worth to you as the guy voting for him?
If enough minor-party candidates get enough votes, maybe it eventually contributes to the decline of the two-party system - but that takes hundreds of thousands of votes across many races, so you're back to the problem of your one vote having negligible impact, just like the guy who voted for a major-party candidate.
Alternatively, instead of taking two hours off to stand in line and vote, go home with two more hours' worth of wages in your pocket. Which is the better expected value?
@khird Well no, im not talking about ballot access alone, or even bragging rights.
Most people will not vote for a third party because they feel voting for a aprty with a small chance of winning is a waste of a vote. Therefore by voting third party you increase the number of people that voted for the party and thus with larger portion of support people who use the above logic as a reason not to vote third party no longer have a valid excuse and thus will be more likely to vote third party int eh future.
So while ballot support is one element worth considering the argument is entierly valid even if that factor is not considered at all.
Remember the USA has changed primary parties 9 times in its lifetime. In all cases the changes following non-linear trajectories where the third party had almost no support, there is a marginal increase in support and that increase quickly snowballs, breaking the third party mentalitya nd resulting in a third party replacing a primary party. This has been the pattern in all historic cases.
So by increasing the support of a third party you effect actual good by encouraging the transition of the third party to a primary party due to the perception of the general public, which can have results in only a single election year based on historical observations.