Wikipedia: First-past-the-post election system

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An election voting system for single-member districts, variously called first-past-the-post, plurality voting, or relative majority. This system is widely used at all levels of politics - famously in Great Britain and the United States. For a thorough list, see below.

Voting

Each voter selects one candidate.

Counting the Votes

All votes are counted and the candidate (or proposal) with the most votes is declared the winner.

An Example

4 candidates: Andrea, Brad, Carter, and Delilah.

35 voters choose Andrea
27 voters choose Brad
16 voters choose Carter
11 voters choose Delilah

Andrea is elected with the most votes.

Potential for Tactical Voting

There is enormous potential for tactical voting. Voters only get one chance to express their preference, so if they express it for a candidate who stands little chance of winning, they do not get to choose between the popular candidates. Because of this, most voters vote for the candidate they prefer among those candidates who they believe have a chance of winning. Therefore, candidates often vie to seem like they are likely to win, rather than that they are preferable.

To counteract tactical voting, sometimes groups of similar-minded voters will hold preliminary, or primary, elections amongst themselves to choose a candidate for the true election. This ensures that their vote will not be split amongst similar candidates. Sometimes this is institutionalized in the form of a political party.

Another potential downfall of this system is that the winner does not have a majority, and in fact often does not. Possible solutions to this problem is found in runoff voting and instant runoff voting.

Where it's used

Countries that use this system to elect the lower or only house of their legislature:

Bahamas -- Bangladesh -- Barbados -- Belize -- Botswana -- Canada -- Dominica -- Gambia -- Grenada -- Jamaica -- Micronesia -- Nepal -- New Zealand -- Papua New Guinea -- Saint Kitts and Nevis -- Saint Lucia -- Saint Vincent and the Grenadines -- Solomon Islands -- Trinidad and Tobago -- United Kingdom -- United States -- Western Samoa -- Zambia

Source: Making Votes Count, Gary Cox (1997)