This depends on the state in question (meaning, are you talking about US States, or actual other nations?)
Presuming the question refers to the Primary elections of U.S. Presidential candidates, the answer is that it is NOT up to the states. Primary elections are party-specific; that is, while the state runs the election, the results are up to the party to determine.
Both the Republican and Democratic party in the U.S. do proportional allocation of delegates in primaries. That is, the two major parties set a fixed number of delegates to their national convention, and then allocate a certain number to each state (plus what are called "superdelegates", which are effectively national-party selected). The percentage results of a given candidate net that candidate the same percentage of delegates allocated to that state.
Thus, let us say that the Republican Party has 1000 total delegates. 900 are divided amongst the states (usually by something approximating relative population amounts), so let's say California gets 80 and Delaware gets 10. If Candidates A, B, and C get 40%, 40%, and 20% (respectively) of the vote in CA, they would then get 32, 32, and 16 delegates. If they got 30%, 30%, and 40% (respectively) in DE, they would then get 3, 3, and 4 more delegates.
If the election in question is not for President, but for a state-specific post (including US Senators and Representatives), most parties declare the winner to be the one with absolute most votes, even if it wasn't a majority (i.e. 50% + 1 vote). US elections very, very rarely use a runoff format. And, once again, U.S. Primary election results are for the Party to determine how to interpret. Legally, there is nothing to prevent a Party from nominating a person who received fewer votes than other opponents. Party politics are solely internal.
The primary elections are for delegates to the National nomination convention. Not all states have them and the way in which they select delegates varies. Sometimes the delegation is divided in proportion to the vote, sometimes the one with the most votes get all of the delegates. Sometimes the primaries are only advisory information for the delegates. If no candidate has a majority of the bound and committed delegates by convention time, delegates are all free after the first ballot to vote as they choose. Ballots are taken and deals are made and delegates switch votes until finally one candidate has a majority.
closed primary
Depending on the type of system, various outcomes occur. Some systems have the person with the most votes win regardless if it is not over 50% of the vote. Some systems go to a run-off election. Other systems go to a different type of election or judges to determine the result.
By caucus of members of a political party, by state party conventions, or by primary elections, or by all of the above in some states.
The number of electors required to win the presidency in the United States is 270 (as of 2014). The candidate has to receive the absolute majority of the votes.
a runoff primary is held
a runoff primary is held
a runoff primary is held
The answer depends on the party and the state. Some states have a non-binding primary, some states apportion their delegation according to the primary percentages and some states give all of their votes to the candidate who wins a plurality in the primary. Some parties have some "super delegates" who decide for themselves how to vote.
Some states require an actual majority of the votes to win, while others will elect based on the largest plurality. In the states that require a majority to win, the top two candidates will face a runoff election generally about a month later.
The primary elections are for delegates to the National nomination convention. Not all states have them and the way in which they select delegates varies. Sometimes the delegation is divided in proportion to the vote, sometimes the one with the most votes get all of the delegates. Sometimes the primaries are only advisory information for the delegates. If no candidate has a majority of the bound and committed delegates by convention time, delegates are all free after the first ballot to vote as they choose. Ballots are taken and deals are made and delegates switch votes until finally one candidate has a majority.
closed primary
Iowa doesnt have a primary because it is usually the bigger states who have primaries, the smaller states usually get together to decide the states candidate, which is what a caucus is.
Depending on the type of system, various outcomes occur. Some systems have the person with the most votes win regardless if it is not over 50% of the vote. Some systems go to a run-off election. Other systems go to a different type of election or judges to determine the result.
A majority or plurality of votes.
By caucus of members of a political party, by state party conventions, or by primary elections, or by all of the above in some states.
These are called primaries or primary elections. Not all states have them.