Voting Systems: Why Winner Isn't Liked by Majority

By Xah Lee. Date: 2012-08-13

Voting system is inherently mathematical. It's quite complex. For example, majority does NOT always win! Also, there's undesirable side-effects. For example, the common system familiar to most of us, called “Plurality Voting”, where each voter selects one candidate, will create a situation where it's effectively like there are just 2 candidates. (a practical example of this is USA's Republican Party vs Democratic Party)

Winner ≠ Liked by Majority

Winner isn't necessarily liked by majority. Here's a example. Suppose there are 3 candidates: {A, B, C}. A gets 4 votes. B gets 3. C gets 3. So, A is the winner, but only 4 out of 10 voted for him.

2-Party Situation

Common voting system creates 2-party situation. Here's a example.

Suppose there are 5 candidates: {A, B, C, D, E}. Now, usually voters have some info about which canditates are top contenders. So, suppose, person C is not popular. Now, those who support C will not likely to vote for C, because it's most likely a waste of vote. So, the focus will be the top 2 contenders — a 2-party situation.

This is interesting, because even if you like C, you are forced to not vote for C, unless C likely to be among the top 2. This means, there's something inherently “wrong” with the 1-person-1-vote system.

Here is a quote from Wikipedia Duverger's law:

To a much greater extent than many other electoral methods, plurality electoral systems encourage tactical voting techniques, like “compromising”. Voters are pressured to vote for one of the two candidates they predict are most likely to win, even if their true preference is neither, because a vote for any other candidate will likely be wasted and have no impact on the final result.

Basic Types of Voting Systems

There are many types of voting systems, some avoids the above problems created by simple 1-person-1-vote system. Here's the basic types:

Plurality voting (aka “first-past-the-post”) → each voter select one candidate. Winner is the one with the most vote.
Approval voting → each voter select as many candidates as they want.
Ranked Ballot (aka “preference”) → Each voter order the list of candidates from most to least preferred.
Range voting → each voter rates each candidate separately on a scale (For example, score the candicates).
cumulative voting → each voter may vote for the same candidate multiple times.