USA Presidental Election – Expected Outcomes of Votes

Many voters consider both Donald Trump and Hillary Clinton to be extremely bad potential presidents, yet consider one to be far worse than the other, and so think they should vote for Trump, to help ensure that Clinton isn’t elected, or conversely, vote for Clinton, to help ensure that Trump isn’t elected.

This attitude, I believe, fails to take into sufficient consideration the effect a vote in 2016 will have on the candidates in 2020, 2024, etc. Since we can expect be a presidential election in the USA to occur in those years as well, in assessing a vote overall, we have to consider the influence a vote made now has on what kind of candidates we will likely have in 2020 and subsequent election years.

Basically, a vote for either of the two major parties’ (bad) candidates increases the likelihood that one or both of those parties puts forth similar (similarly bad) candidates in 2020, 2024, etc. Such a vote is a “vote” for the “system”, so to speak — it not merely supports a particular candidate, but supports one or both of those major parties in putting forth in the future the kind of candidates they have this year.

In more detail: Assuming the vote between Trump and Clinton is close: a vote given for either of these two candidates (rather than a third party candidate significantly better than either of them) is a strong support for having two similar candidates to the current ones in 2020 (and in 2024, and 2028). For, to the degree that the major parties get more votes, they have little motivation to change significantly.
Assuming that one candidate, e.g., Hillary wins by a large margin: a vote for that candidate (rather than a third party candidate or for the other major party candidate) is a slight opposition to having a republican candidate similar to Trump in the future, and a slight support to having a candidate similary to Hillary in the future.

By “support” for a future outcome I mean that an action in fact increases the probability of a given outcome, and by “opposition” to a future outcome I mean that an action in fact decreases the probability of that outcome.

So, the more likely your vote might be the deciding vote between Trump and Clinton, to that extent your vote is simultaneously a vote (i.e., supports) having two candidates similar to them in 2020 (and in 2024, and 2028, etc.)
The less likely that your vote is unlikely to be the deciding vote between Trump and Clinton, to that degree your vote for one of them is less likely to affect the future major party candidates in 2020. (In addition, one influence of your vote in this respect is good, the other bad.) Consequently, to that degree does the value of a vote for a third party in supporting major party candidates in 2020 different from the current ones, outweighs the positive value of a vote for one of the major candidates.

To sum up, whether or not the race between Trump and Clinton is close, a vote for either one of them rather than for a third party candidate who would be significantly better than either of them, has a much greater expected negative value due to its expected probable influence on the 2020 (and 2024, 2028) candidates, than the expected positive value in hindering the “worse evil” 2017-2020.

The rigorous game theoretical proof of this is left as an exercise to the reader.