Is a majority a majority?

Maybe I am taking it too far but let me try this way: 1 million people vote to have a king come rule over them and 1 million vote to not have a king come and rule over them, the vote is a tie, so no king comes and rule over them. Even though the vote was a tie so nothing was able to get done, it would seem that the million who voted for no king actually won with no majority!
Now, one person comes along and votes for no king, that is a majority vote for no king it would seem but was this vote really necessary? no king was coming anyway because of the tie vote.
But had he voted yes for a king, somehow it now matters and is considered a majority vote.
This is why I say that one vote decided the outcome. hmmm
I see what all you are saying but this scenario just seems weird to me.
Maybe it is a weird way I am looking at the world.
(BTW all this started thing about the brexit vote, but I was generalizing it)
virtually yours

In the US Senate the VPOTUS votes to break ties. He can be said to decide which way the Senate votes on a bill. But he only gets to vote after the tie has occurred, otherwise he has no vote.

If you can count all of the 2 million votes cast and if they tie then you get to pull in the designated tiebreaker then that person’s vote will decide the issue. But unless you set up the voting process so that you count the votes and then ask the designated tiebreaker to vote then there’s no way to identify which of the 1 million and one votes was the one to put you over the top. They all put you over the top.

As to your last point, ties don’t happen in elections for office, there are tiebreakers for that even if it’s just flipping a coin. They only happen in Supreme Court rulings, ballot questions, and some legislative bodies. In most cases if there is a tie, no action is taken because of convention. But that doesn’t seem central to your argument.

Exactly. If 2,000,001 people vote together (i.e., in the same election), and once the votes are all tallied, 1,000,0001 votes are “for”, while you can say that “for” won by a single vote, it’s impossible to say which one of those votes was “the deciding vote” – and, by extension, you also can’t say that any one voter “decided” the result of the election for everyone.

If (and this is purely hypothetical, of course), the total number of voters is that same 2,000,001 people, but only 2,000,000 vote at once, the votes are tallied, and the result is a tie…and then voter 2,000,0001 is allowed to cast a deciding vote, then and only then could you say that one particular voter is deciding the outcome for everyone.

This sort of thing certainly can happen in legislatures – such as if the U.S. Senate is deadlocked at 50/50, at which point the Vice-President, knowing that the vote is deadlocked, can then cast a tie-breaking vote. But, generally, when we’re talking about regular citizens and voting, I think it’d be rare in the extreme for some voters to be allowed to cast their votes after everyone else’s votes have been tallied and announced.

Yes, it is the way you are looking at the world. That one person you identify as having decided the issue wouldn’t have decided the issue if those other votes hadn’t been cast as well.

If 2,873,685 people voted to have a king and 2,873,684 people voted against having a king, did somebody cast the deciding vote? How do you decide which person it was?

Suppose 1,500,000 people voted to have a king and 1,100,000 people voted not to. The pro-king group won by 400,000 votes. If those 400,000 people had voted the other way does that mean they decided the election? If so, how do you pick out the 400,000 people who cast deciding votes from the 1,500,000 people who all voted the same way?

If we set Numbers aside, does that mean we jump to Leviticus?

Thats for direct voting. And the laws make it clear how to count, rather then leaving you to interpret words like “majority”.
However in Congress/Senate/Parliament etc… there can be the situation that the parties are facing off and they can talk about the “balance of power”, who is the group or individual who is the swinging voter…

Party A, 30 reps
Party B 30 reps
Independent C, 1 rep

The independent then has balance of power … and can get more than 1/60th the attention because his vote is the deciding vote between the two parties. Worried the OP confused talk of this situation with the public voting.
But yes the OP is right to say that since there is one president, and two candidates, the winner could win by just one vote.

The president could win with only 40% of the vote because of the way the votes are tallied state by state and a number of electors then represent the state at Washington DC electoral college. Many states have winner takes all for the electoral college people… win the state, win the states electors… eg if its a 10 elector state, the winner of the state wins 10. Rather than say, win 65% of the vote, win 6.