If you could choose how to reform the Presidential Elections, what would it be?

[Verily]

Two votes is just another prop for two parties; you could do approval voting, which is the equivalent of having any number of votes but can only vote for each candidate once, but that tends to result in unknown candidates doing well, which may or may not be a good thing.

Strict IRV is fine with me, but without electoral votes.

[Verily]

Nationwide IRV poll with a NOTA option.

Why?
A nationwide poll because all citizens should be equal in an election. The value of one's vote for the Presidency shouldn't depend on where in the Union one happens to reside.
IRV because it allows the voter to express his true preferences without concern for wasting his vote; and encourages a greater number of candidates to stand giving the voter greater choice.

Greetings to Ireland! I wanted to ask you if you could explain how the ballots are, voting counting (manual or machine) and is there some sort of fee or number of petition signatures candidates in Ireland need to get when they run for Pres? Thanks

My impression is that Irish Presidential elections are only occasionally contested and never competitive, partially because the President has few powers.