Wasted vote

In electoral systems, a wasted vote is any vote cast that does not impact the final election outcome.

Terminology
There are two different types of wasted votes: Sometimes the term "wasted vote" is used by those referring only to "lost votes", while others use the term to refer to the sum of the lost votes and the excess votes.
 * Excess votes are votes that a candidate receives above and beyond what was needed.
 * Lost votes are votes that were not enough to make an impact by winning a seat.

Plurality voting
In plurality systems, the ballots of voters outside of the plurality are considered "wasted" as they do not contribute to the final outcome. This is because the wasted votes include both "lost votes" for all candidates not finishing first, as well as the "excess votes" for the winning candidate beyond what was needed to win.

Comparing wasted votes between parties in legislatures determines the efficiency gap measure, which quantifies the bias in allocating voter preferences due to the shape of electoral districts. A non-zero efficiency gap indicates disproportionally more wasted votes for one party. The efficiency gap may be the most discussed method of measuring gerrymandering.

Proportional representation
In proportional electoral systems, representatives are elected in rough proportion to voter preferences, resulting in fewer wasted votes than in plurality voting.

Thresholds and lost votes
The wasted vote includes the total number of voters not represented by any party sitting in the legislature (or unrepresented voters). The wasted vote share is calculated as: $v_{wasted}=\sum_{i=1}^nv_i$ where $$v_i$$ is the vote share of unrepresented party $$i$$ and $$n$$ is the overall number of unrepresented parties. The lost vote can be given as a percentage of the total number of votes or as the absolute number of votes. Wasted votes in proportional representation increase with a higher electoral threshold. Decreasing district magnitude (electing fewer members in the contest) is one of the ways to reduce political fragmentation in the chamber. Even with no explicit electoral threshold, the natural electoral threshold causes some wasted votes and produces more disproportionality. That is why the more members being elected in the contest, the more fair the result.

On occasion, lost votes in proportional representation (arising from high electoral threshold) result in a party winning an outright majority of seats without winning an outright majority of votes. For instance, in the 2002 Turkish general election, the AKP party won more than two-thirds of the seats in the Turkish Parliament with just 34.28 percent of the vote due to a large election threshold of 10%. In the 2013 Bavarian federal state election in Germany, the CSU party failed to obtain a majority of votes but won an outright majority of seats.

Ranked voting
Ranked voting, unlike traditional plurality systems and list PR systems, allow voters to redirect what would otherwise be a wasted vote to other candidates. The goal of ranked voting is to reduce the waste that occurs in many elections due to votes being cast for unsuccessful candidates or by the existence of winners' excessive leads over their nearest contenders. Quota, a majority of votes cast, or at least a majority of votes still in play when the seats are filled, are used to elect under ranked voting systems. However, in single-member ranked voting (also known as instant-runoff voting), a portion of votes will still become wasted votes if cast for the last-surviving losing candidate or by being cast for the winning candidate if that candidate received votes in excess of what they needed to win. But at most this will be less than half the votes in the counting, which is considerably fewer than some first-past-the-post elections where two-thirds or more of the votes may not be used to elect the winner.

When not all candidates are ranked by every voter, ranked vote systems can produce exhausted ballots – ballots that could have been redirected to lower preferences if the ballot had been fully ranked. In multi-member ranked voting, wasted votes are less common compared to single-member ranked voting. The number of votes not used to elect someone is commonly the same as one quota (usually the Droop quota is used).

A vote can also be thought of as at least partially wasted when a vote has been given to a candidate who is a lower preference for the voter than a higher-ranked candidate. For instance, the Australian Electoral Commission tells voters that "there is no such thing as a wasted vote" due to preferential voting preventing votes from finishing in third place or lower, in cases where the last runoff was between only two candidates. However, a large share of votes in Australian lower-house elections are excess votes for the winning candidate or partially wasted votes that were used to elect a lower-ranked preference. These instances of waste occur more often, however, under first-past-the-post.

Cardinal voting
Cardinal voting or score voting methods can reduce wasted votes.

Strategic voting
Strategic voting is a voting approach that attempts to reduce the chance of a vote being wasted. Election campaigns focus on swing seats because votes gained in swing seats are more likely to result in increased representation and thus not be wasted. In election campaigns, a leading candidate may appeal to voters who support a less popular candidate to vote instead for the leading candidate for tactical reasons, on the basis that a vote for their preferred candidate is likely to be wasted. Excess votes for more popular candidates allow less popular candidates to make similar appeals to supporters of more popular candidates.

An electoral system which reduces the number of wasted votes can be considered desirable on grounds of fairness or because of the danger that voters who feel their votes make no difference may feel detached from their government and the democratic process.

Example 1
Consider an election where candidates A, B and C receive 6000, 3100 and 701 votes respectively.

If this is a plurality voting election for a single seat, Candidate A has a plurality of votes (actually a majority) and is therefore elected. The wasted votes are:
 * All 3801 votes for candidates B and C, since these "lost votes" did not elect any candidate
 * In the wider definition, the 2899 excess votes for candidate A are wasted, since A would still have won with only 3101 votes. Therefore, 6700 out of 9801 votes are wasted.

If the same votes for A, B and C are cast in a d'Hondt method election for 2 seats, then the seats are split 8-4-0 for A-B-C. The wasted votes are:
 * All 701 votes for party C, which won no seats.
 * In the wide definition, also wasted are:
 * 399 votes for A, since A would still have won eight seats with only 5601 votes against 3100 and 701 (with 5600 votes for A, the last seat would go to C)
 * 299 votes for B, since with only 2800 votes, B would lose the last seat to C

A majority of votes are wasted in a single-seat plurality election. Multi-seat constituencies reduce the number of wasted votes as long as proportional representation is used. (When used with winner-take-all systems, multi-member constituencies may still see the wasted vote exceed 50 percent.)

Example 2
Consider an election where candidates A, B, C and D receive 6000, 3100, 2400 and 1701 votes respectively.

If this is an instant-runoff voting election for a single seat, no one has a majority of votes so Candidate D is eliminated and the votes for them are transferred. If over 600 of them go to A, A has a majority and is declared elected; if instead the vote transfer from D did not produce a majority winner, then C would be eliminated (or B if C's vote total has surpassed B's) and either A or B (or C) would have a majority and would be declared a winner. The wasted votes are:
 * 6600 at the most and potentially as few as 4300

If this is a vote using the single transferable vote for two seats, the Droop quota is 4400. Candidate A has that in the first count and is elected. Transfer of A's surplus may give B a quota and victory; otherwise, D is eliminated. It is likely that the second seat would be filled by someone with quota, hence wasted votes would have to be less than a third of votes cast. If two win seats by having quota, the wasted votes are one quota at the most so likely: It could be that the second seat is not filled by a candidate with quota, but by the candidate who is merely the most popular when the field of candidates thins to two. If so, the number of effective votes could be no greater than 4101, but that would assume a great number of exhausted votes. But even so, the wasted votes could be:
 * less than 4400
 * no more than 4101

Historical examples
In the 1993 Polish election, the wasted vote reached 34.4 percent. The use of electoral thresholds, set at 5% for party lists and 8% for coalitions, resulted in some parties not being eligible for representation.

In the Russian parliamentary elections in 1995, more than 45 percent of party votes were wasted, due to the 5 percent electoral threshold. Nineteen of the parties that did not exceed the electoral threshold did win district seats so did have some representation. In 1998, the Russian Constitutional Court found the threshold legal, taking into account limits in its use.

In the 2002 Turkish general election, as many as 46.33 percent (14,545,438) of votes were cast for parties that went unrepresented in the parliament. An unusually large electoral threshold of 10 percent prevented all but two parties from taking seats. The justification for such a high threshold was to prevent multi-party coalitions and put a stop to the fragmentation of political parties seen in the 1960s and 1970s. However, coalitions ruled between 1991 and 2002, but mainstream parties continued to be fragmented; in the 2002 elections, as much as 45 percent of votes were cast for parties which failed to reach the threshold and were thus unrepresented in the parliament. All parties that won seats in 1999 failed to cross the threshold, thus giving Justice and Development Party 66 percent of the seats.

In New Zealand, the wasted vote was only 1.5 percent in the 2005 general election, 4.62 percent in the 2017 election, and 7.71 percent in the 2020 election.

In the Ukrainian elections of March 2006, 22 percent of voters were effectively disenfranchised due to an electoral threshold of 3 percent of overall votes, including invalid votes. In the 2007 Ukrainian parliamentary election held under the same system, fewer voters supported minor parties and the total percentage of disenfranchised voters fell to about 12 percent.

In Bulgaria, 24 percent of voters cast their ballots for parties that would not gain representation in the elections of 1991 and 2013.

In Germany in 2013 15.7 percent or 6.9 million votes were unrepresented.

In the 2015 Israeli legislative election, the wasted vote was 7.1 percent. The election is held with the country as a single district, which reduces the potential effective threshold to a minimum but an electoral threshold of 3.25 percent means that some minor parties did not get representation.

In the 2015 Danish general election, where MMP was used, the wasted vote calculated by the formula above in Denmark proper was 0.92 percent. The wasted votes in Faroe Islands and Greenland, referred to above, made up a very small proportion of the total 3.5 million votes cast across the country.

In the Netherlands, the wasted vote was 1.55 percent in the 2017 general election and 1.99 percent in the 2021 election. The low percentage of waste in the Netherlands was caused by a low electoral threshold. The threshold is set at 0.67 percent, which is the same as the effective threshold produced by electing 150 seats in a single district covering the entire country.

When districts are used under PR, waste of district votes may occur. During Danish general elections in 2015 and 2019, in the Faroe islands, where only two members were elected and 23,000 votes cast, the waste of votes reached 51.3 percent (11,000) in 2015 and 46.2 percent in 2019. In Greenland, where two were elected and 20,000 votes cast, in 2015 21.96 percent (4300 votes) and in 2019 34.2 percent of Greenland voters were not represented in the Parliament of Denmark.

In the 2019 European Parliament election in France, 19.79 percent of voters were unrepresented. In the 2020 Slovak parliamentary election, 28.39 percent of all valid votes did not gain representation. In the 2021 Czech legislative election, 19.76 percent of voters were not represented. In the 2022 Slovenian parliamentary election, 24 percent of the vote went to parties that did not reach the electoral threshold. In the German federal state of Saarland 2022 election, the total wasted vote was 22.3 percent. In the 2022 Latvian parliamentary election, unrepresented voters reached 29 percent.

Examples of low wasted vote are the 2018 Swedish general election with a wasted vote of 1.5 percent, and the 2019 Swiss federal election with a wasted vote share of 1.3 percent, caused by natural electoral thresholds.

Legal status
High wasted vote in plurality systems as measured by the efficiency gap has been found illegal in some cases.

For proportional representation, the German Federal Constitutional Court rejected in 2011 and in 2014 an electoral threshold for the European Parliament that led to wasted votes based on the principle of one person, one vote. In the case of Turkey, the Parliamentary Assembly of the Council of Europe declared in 2004 the 10% electoral threshold excessive and asked Turkey to lower it, which would reduce wasted votes. On 30 January 2007, the European Court of Human Rights ruled that the 10 percent electoral threshold in Turkey does not violate the right to free elections guaranteed by the European Convention of Human Rights. It held, however, that this same threshold could violate the Convention if not justified. It was justified in the case of Turkey in order to stabilize the volatile political situation over recent decades.