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If I'm voting republican in a state such as California, does it even matter?

I decided not to vote since CA is overwhelmingly blue and I thought my vote would be pointless

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  • We already have a question which describes the same situation but with the roles reversed: A Democrat living in a red state. But whether you are a Democrat in a red state or a Republican in a blue state doesn't really change the conclusions. I therefore closed this question as a duplicate. – Philipp Nov 6 '20 at 9:44
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    Why should anyone vote? A Republican in Texas is also unlikely to make a different by voting, right? Or a Democrat in California? – user253751 Nov 6 '20 at 13:58
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The probability that your vote will affect the outcome is only one way of looking at the situation. There are a number of other reasons why you should go out and vote, even if you live in a safe seat/state.

You can find arguments for voting in safe seats all over the place. Why am I being asked to vote

Arguments on Voting counts are based on UK numbers, but the same follows in most places.

In 2017 there were 14.5m non voters, that’s more potential votes than any one party received. If all of these people went to the polling station, then the outcome could be very different – even in constituencies seen as ‘safe’.

In 2016 in California if everyone who didn't vote had turned up and voted Trump, then Trump would have won. Actually it's worse than that. If all those votes had turned out and voted for me, then I would have won. Which would lead to some tricky eligibility questions...

Turnout 58.74%   
Nominee            Votes        Percentage  
Hillary Clinton    8,753,788    61.73%    
Donald Trump       4,483,810    31.62%  
Did Note Vote      9,298,320    (70% of number of people who voted)

There's an LSE blog post with 5 reasons. Again the details are UK, but the principles apply across the world. I've just cribbed the headers, follow the link to the full piece.

1: The seat might not be as safe as you think
2: To influence your MP’s behaviour
3: To make future elections more (or less) competitive
4: To influence national vote share
5: To help keep democracy alive

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This paper analyzed the probability that your vote would affect the presidential election outcome based on information available before the 2008 election. Obviously, the electoral landscape changes from year to year, but California has been fairly blue for a while now, so perhaps this can give us an idea of what these probabilities might be like.

Figure 3 gives a nice exposition of the probabilities. Figure 3

It shows that for California in this year, your probability of affecting the election would have been about 1 in a billion. This makes the expected number of Americans for whom you would have changed the president about 1/3. If you lived in another state like Virginia, you would have changed the president for 30 people on average. Whether this is "worth it" is a subjective decision.

This is also to say nothing of your vote's potential to affect other federal, state and local elections.

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