I am a Democrat living in a solidly Republican state. I have tried to research this, but I only get the standard opinion that I should vote no matter what. Same with people I talk to.
Is there any evidence (research, proofs, papers) arguing that my vote is important in the November election? Will it make a difference?
It might seem like when you belong to the minority in your state then voting does not matter. And when you only think ahead for one election-cycle you are right: In the voting system of the United States it does not matter if a candidate wins a state by 70% or 51%.
But keep in mind that some of the states which are considered red, blue or flip-states today weren't always that way. The political orientation of states can change over the course of several decades. But unless the current minority keeps voting for their party this is not going to happen. While a slight improvement of the vote-percentage of your party will not make any difference in the current election, it sets a signal for future elections that your state drifts further into the direction of political middle-ground and might become more relevant in future elections.
Besides the point of @Philipp, there is another very important point.
A democracy works if people vote - that's the whole point between a democracy. It's there so that everyone can share their own political belief and to find compromises among them to find the best solution for everyone. In the end, the democracy we today know was introduced to restrict crazy monarchists and emperors who didn't care about the average citizen.
If you know vote, what you absolutely should, you can show your belief and that's what it is about.
For example: I am a politician from a party and my party wins by a 30% or even greater margin. I then look into the poll and see that there are roughly 40% non-voters of the population in my state. I can now conclude that these 40% don't care about politics as they didn't see the need to vote. So I know that I don't need to expect any uproar or unrest from them if I pass a law.
Of the other 60% voters, 70% voted for me and 30% for other parties. This means that I can pass laws as I like because
Another scenario would be if I won just by one percent - so I got 51% and the others 49%. You may now say: won is won. But it's not. These results show a clear uncertainty among the people in your state as they don't know what is "right". And in this case, I must pass laws that favor them and me because
Why do you think minorities are such a important word in politics? Blacks, hispanics, religious people, atheist people, racial tension and so on. You must take care of minorities because if you do not, you can expect to be faced with social unrest and eventually violence and this leads into this embarrassing situation that other states or nations become slightly suspicious of your ability to lead your people. The word minorities was invented to protect people who are in a minority so they can't be taken advantage of by the majority.
A democracy means political engagement and this is the whole point of it. The moment you don't vote I can consider that you simply don't care about politics anymore, meaning that you wouldn't necessarily need a democracy. Different ideas and opinions must merge in a democracy or you have no democracy. In order to voice your opinion, you are required to fill your voting sheet.
If you not, I will become the next presidential candidate in your state and burn down democratic ideas and ideals, and don't you dare to even think about revolting - you didn't even vote in the beginning!
It does matter in a variety of ways:
Presidential elections usually coincide with lower level (state, local) elections.
If you don't go vote, you're excluding yourself from those lower level elections. Those local elections can be far more competitive even in solid-blue/red state; and voting in them can make a difference.
While "who wins" is of course important, and for that, only electoral math matters in USA, the concept of "mandate" still has political meaning, and popular vote is often seen as a proxy for that.
See the whole "Bush" thing in 2000 elections as an example - he clearly won electorally (even if SCOTUS ruled against him, he'd have won as it was shown later), but people have been challenging that for the past 16 years, in large part because of popular vote.
As another answer alluded to, "solidly Republican/Democrat" is not really a law of nature. Things change, and unless everyone votes, you wouldn't be able to see that change and assess it.
If 100,000 voters of "not popular" party ALL not vote because it's futile, then it distorts "real" voter sentiment.
Voting has this odd dynamic where when you try to analyze it a personal level, it seems like your vote doesn't matter, but when you analyze it at the collective level, it matters a lot.
Suppose the election of the Democratic candidate, makes a moderate to low difference in your quality of life. If you naively calculate benefit you get from that candidate, and scale it to the odds of your specific vote being the deciding factor, and weigh that against the time you spend going to your polling place and voting, you will calculate that it is not worth your while to vote.
However, if literally all the Democrats in your State vote for the Democratic candidate, there is a surprisingly strong chance that the Democratic candidate will win, and assuming you all get a similar benefit, it will have been collectively worth your while.
The Democratic candidate simply won't win if you, and people like you don't vote. If you and people like you do vote, then even though there's not going to be a 100% chance that you win, you do have a chance
"...I should vote no matter what..."
That's the right idea because otherwise your state will very probably remain solidly Republican which you probably do not want. Your vote could make the current balance of power look less solidly Republican and that in turn can make the difference for the next election.
Also a miracle may occur and the Democrats may take this state by surprise. This miracle would probably have to involve for a lot of people voting for the Democrats and for this you better be one of them.
Maybe many Democratic leaning voters have just given up in your state and if only they would vote, things could look different. If you give up before the race is actually going to take place, you cannot win. That's probably against the spirit of elections.
In short: Voting is a privilege and should always be exercised, even if the gain seems low, because the impact will be above zero. Compared to the cost of voting the value seems reasonable.
There is no state more solidly Republican than Texas, and yet the latest polls show that Hillary is only a few points behind Trump in Texas. So, voting for Hillary would make sense.
I hate to say it but your vote probably won't make a huge difference in the results if it's a solidly Republican state.
However, it does contribute to the overall popular vote of a candidate. Since everyone has the mentality that it doesn't make a difference, it makes it very difficult for the state to flip. If everyone in the minority decides to vote, though the candidate might not win, it will increase the popular vote of the candidate.
For the record, the only states that hasn't flipped since 1972 are Alaska, D.C., Idaho, Kansas, Nebraska, North Dakota, Oklahoma, South Dakota, Utah and Wyoming.
But, in this election, some pundits did say that Utah might be contested, though it's a solid Republican state. So, even if it might not have a large chance of flipping since Trump is still leading, there is still a change of flipping.
Also, North Carolina is also considered a solid Republican state, but Obama won it in 2008 anyway.
Also, in addition to the states listed above, here are some example of states that are considered solid in the past but flipped after the 1992 landslide victory for the Democrats: California, Connecticut, Delaware, Illinois, Maine, Maryland, Massachusetts, Michigan, New Jersey, New Mexico, Vermont.
At that time, people probably won't thought that their votes counts a lot but it did.
So, in conclusion, I do think that voting matters even if it might not affect this year's election. It might be useful, who knows that Obama would have won North Carolina in 2008?
In your situation, not voting can be very detrimental.
In every election, the totals are published, and both politicians and the general public pay attention to those totals.
If a lot of Democrats in your state don't vote, then the assumption will be that there aren't many people in your state who object to the Republican platform. This can hamper fundraising.
On the other hand if every Democrat in your state votes, you might find that the state isn't quite so red after all. Your party will have an easier time organizing and fundraising, if they see that they have a better chance of winning.
By not voting, you make your position even less important.
Since the 2010 elections most states legislatures were in republican hands for the redistricting following the census and gerrymandered the hell out of all those states to maximize republican votes in the future. I will always go to vote but I realize that my vote for a Democratic president will not count.
Analysts can say all they want that it matters in the long run as the winning candidate can decide how much of America supports them by how big a margin they won by. Our current president who was elected with the minority of popular votes could care less about those who are not part of his base as those are the only Americans he feels he must satisfy. So the point about whether your vote for president in a solidly red or blue state doesn't hold water. The only reasonable option is to get rid of the electoral college altogether.
This does not even address how a vote for president in a state with very small populations counts considerably more than a person's vote from a very populous state. Tell me why a vote in Wyoming should be worth more than one from NY or California.
