Option 1. Any other choice is a probabilistic injury to yourself. A very simple rule of thumb for voting is that you should always vote whenever possible and always vote for your most preferred option.
The reason to do so is as follows. Your overall most preferred candidate, that being the one you want to see ultimately win the election, has a certain degree to which you'd prefer he'd win. You might like him a lot or you might like him a little, but there is some value that he is worth to you. This is akin to the pay off on a bet. To assign arbitrary numbers, he/she could be worth $20 to you or $100, and whatever this amount is it is the highest pay off available to you in your betting pool. Let's say this is Jophiel making the bet and that Obama is his primary choice. Since the Democrat candidate is decided we can ignore other democratic candidates. Obama is worth $50 to Jophiel.
Now Jophiel has the decision whether to vote in the GOP primary or which candidate to vote for if he choose to do so. Each of these candidates is not Jophiel's most preferred candidate, and therefore presents an opportunity cost. This is akin to the value of losing a bet. Let's simplify it to just 2 candidates: Mitt and Rick. The same is true regardless of the size of the candidate pool. Let's pretend that of these two Jophiel prefers Mitt over Rick. Mitt is worth -$30 to Jopiel and Rick is worth -$70. First of all, Jophiel must vote. To not vote is stating that all options are equally preferable to you, which is almost never true. So Jophiel must vote, who does he vote for? Any vote Jophiel casts increases the candidates odds of winning the primary, and since this is the most he can do to affect the primary results this is akin to picking a candidate to win the primary. So we can simplify this to saying Jophiel gets to straight up pick the winner of teh GOP primary, wow you've got a lot of connections Jophiel.
So who does Jophiel pick? Jophiel has already decided he will vote for Obama in the general election, so now all he can do is choose who Obama faces. Each candidate is polling differently against Obama, and we can say that this reflects their odds of winning against Obama. So picking a candidate is akin to choosing the probabilities of getting Obama over the candidate you picked. It seems then that the simple logic is to pick the opponent which gives Obama the best chance of winning. This is the logic behind "Yes, for whoever I think would be the easiest GOP candidate to defeat." This is bad logic. To show this, let's assign an arbitrary win chance of Obama agaisnt these candidates.
Obama versus Mitt - 55/45%
Obama versus Rick - 60/40%
Ah, but as any gambler knows, you don't just need the odds, you need the payoffs.
Obama versus Mitt - $50 @ 55% / -$30 @ 45%
Obama versus Rick - $50 @ 60% / -$70 @ 40%
So let's do the math.
Obama versus Mitt - ($50*55%=$27.5) + (-$30*45%=-$13.5) = $14 average
Obama versus Rick - ($50*60%=$30) + (-$70*40%=-$28) = $2 average
This is why picking the easiest candidate to defeat isn't always the best option. Because while you increase the odds of the outcome you want, you potentially risk an outcome that is much, much worse. It can be a riskier gamble.
However, I only proved that picking the easiest candidate to defeat isn't always the best option when earlier I said always vote for your most preferred option. Any basic logician can see the first doesn't necessarily imply the second, so now we move on to how I got there.
I presented a case where unpreferred GOP candidate was someone Jophiel really didn't like (-$70 for Rick compared to -$30 for Mitt). But what if we kept the polling odds against Obama the same, but maybe we only like Mitt (now -$60) slightly more than Rick.
Obama versus Mitt - ($50*55%=$27.5) + (-$60*45%=-$27) = $0.5 average
Obama versus Rick - ($50*60%=$30) + (-$70*40%=-$28) = $2 average
Ah so in this case we do end up with averaging out better if we elect Rick in the primary to face off against Obama, even though we still like Mitt more than Rick. So why should we vote for Mitt?
Well, Rick is polling worse against Obama than Mitt, which means fewer people would vote for him, and thus he is the less preferred candidate by the nation. We've already said Jophiel gets to just pick the GOP primary winner, so let's say we let a Republican pick the Dem primary winner the next time an election is up. What happens if he uses the same strategy? Well we end up with 2 candidates who are each less preferred by the nation than either of the other two primary candidates and we are all worse off.
At this point the game becomes a prisoner's dilemma. If we all vote for the person who is easiest for our guy to beat we all lose. However, anyone who has study the prisoner's dilemma will know that one of the most effective strategies for playing it over an iterated session is tit for tat. That is, you cooperate as long as the other person cooperates and cheat when they cheat. You are willing to play nice, yet you aren't taken advantage of. This still clashes with always vote for your most preferred option. How do I resolve this?
Simply, punishment and cooperation in tit for tat only works if people understand what is going on. Punishing people when they don't understand what you're doing or why is pointless. That's why all of the logic posted here has to be boiled down into a consistent and unyielding command that can be easily communicated. People can accept "do unto others as you would have them do unto you" even if they don't understand the nuances behind it.
And thus concludes my very thorough proof of why we must all pick option 1.
