Vote splitting

A split vote, or vote-splitting, occurs in an election when a voter supports more than one candidate but is unable to express their endorsement on the ballot. As such, vote splitting is a consequence of Ballot Type. This means more expressive ballots have less or no vote splitting. Vote splitting is normally defined by either unwanted consequences or strategic voting but is hard to define rigorously. There are a number of criteria related to vote-splitting which are more rigorous.

Single-mark ballot
The biggest issue with a single-mark ballot is that it can cause a high amount of vote splitting. It is particularly problematic in single member plurality elections. However, other systems that still use a single-mark ballot such as Runoff voting still have vote splitting.

A standard example of vote-splitting is when two candidates are similar, so they each get half the votes they would if the other were not running. This is a good example of failing the Independence of clone alternatives criteria. Another issue is that the voter's preferred candidate may be highly unpopular in the constituency. This means that using their only vote on that candidate has no influence on the result and could be better served on a second or third choice. This is a problem of voter impact which can be thought of how clearly a voter's true choice is translated into the election of a candidate. This is often referred to as the Wasted vote problem if they still vote for their favorite or the favorite betrayal problem if they vote for another candidate. This system rewards voters for not voting for whom they really want and as such promotes strategic voting. Furthermore, it implies that the voter's choice will be heavily dependent on their estimates of how others will vote, not on their preference. The use of fake polls or deceptive reporting can have large effects on election outcomes where strategic voting is emphasized. With all systems of voting, the second-order effects of people trying to vote strategically must be considered.

Ordinal Ballot
The major advantage of such a system is to eliminate the standard forms of vote splitting which are present in Single-mark ballot systems. This can largely eliminate issues that give rise to the wasted vote, though most ranked methods do still fail the favorite betrayal criterion.

Unfortunately, it can be proven mathematically that ranked ballots cannot produce a communal preference without serious issues. There are no non-dictatorial rank voting systems that satisfy both Pareto Criterion and Independence of irrelevant alternatives in a way that can produce such a communal preference. This is known as Arrow's impossibility theorem and states that when voters have three or more candidates, no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting Pareto Criterion and Independence of irrelevant alternatives. Both Pareto Criterion and Independence of irrelevant alternatives are well-supported requirements by experts and the general public, though note that IIA is incompatible with majority rule. The main reason that ranked ballots are still proposed as a solution to vote splitting is that the general public is not aware of the Arrow's impossibility theorem. It is mathematically complex and somewhat counter-intuitive in many systems so is easily ignored. There is a large discrepancy between what the voter impact is perceived to be and what occurs in implementation.

Cardinal Ballots
Cardinal voting systems do not have vote splitting. However, some Multi-Member System can still fail criteria related to Vote splitting such as Independence of irrelevant alternatives. Note that in practice, because it is expected that at least some voters will strategically vote or normalize their ballots, that all cardinal methods will fail IIA.

Relation to Proportional Representation
Vote splitting is often conflated with Proportional Representation but they are completely distinct concepts. Vote splitting is related to strategic or expression issues at the time of filling out a ballot by a voter. Proportional Representation is a measure of the outcome of an election. The relationship is that vote splitting is a major cause of reduced Proportional Representation. Systems designed to achieve high Proportional Representation but that still use single-mark ballots often do not reduce the amount of vote splitting but instead mask its effects at the partisan level. A mixed electoral system, for example, still has a single member plurality component with all the vote splitting issues of a full single member plurality system.

Another confusing point is that Proportional Representation is most clearly defined for Single-mark ballots but Single-mark ballots have the largest problem with vote splitting. When one wants to move to a system without vote splitting to improve Proportional Representation a problem is encountered in that it can no longer be clearly defined.

Examples
In the United States, a famous example of a split vote occurred in the 2000 U.S. Presidential Election when Green Party candidate Ralph Nader attracted voters who might otherwise have voted for Democratic Party candidate Al Gore because of the similar left-wing platforms of both candidates. Because of the very narrow margin of victory of Republican Party candidate George W. Bush over Gore, many blamed Nader's candidacy for causing his loss and thus being a spoiler (although the votes that went to the eighth-place candidate in the contested state of Florida could also have potentially covered the split).

In Canada, the Progressive Conservative Party had held power under Brian Mulroney throughout much of the late 80's thanks to a loose coalition of conservative voters in the western provinces and nationalist voters in Quebec. The coalition collapsed, though, and in the 1993 election the right-wing split the votes between the Reform Party and the PCs, with nationalist voters in Quebec flocking to the newly founded separatist party Bloc Quebecois. The result was over a decade of Liberal rule in Canada.

In modern-day Canadian politics, the Reform Party and the Progressive Conservatives have now merged into the United Conservative Party of Canada, and have been in power since 2006. The left-wing now faces the same vote-splitting that plagued the right, with the four left-wing parties being the Liberals, New Democrats, The Bloc Quebecois, and the Green Party. In the past two election cycles (2008, 2011) there have been efforts among left-wing voters to vote strategically to defeat conservative candidates.