# Wasted vote

In electoral systems, a wasted vote is any vote which is not for an elected candidate or, more broadly, a vote that does not help to elect a candidate. The narrower meaning includes only those votes which are for a losing candidate or party. The broader definition of wasted votes includes votes for winning candidates in excess of the minimum needed to win.[1]

Wasted votes are the basis of the efficiency gap measure of gerrymandering, where voters are grouped into electoral districts in such a way as to increase the wasted votes of one political faction and decrease the wasted votes of the other.

In proportional representation representatives are elected at least in rough proportion to voter preferences, resulting in generally fewer wasted votes than in plurality voting.[2]

Even more broadly, a vote is said to be a qualitatively wasted in the judgment of the voter when their vote has been needlessly added to a candidate who is less valued than a more valued and available candidate.[3]

## Rationale for wasted votes concept

An electoral system which reduces the number of wasted votes can be considered desirable on grounds of fairness or on the more pragmatic basis that a voter who feels their vote has made no difference may feel detached from their government or lose confidence in the democratic process. The term "wasted vote" is especially used by advocates of systems like Evaluative Proportional Representation (EPR) in Section 5.5.5 in Proportional Representation, approval voting, the single transferable vote, two round systems or instant-runoff voting which purport to reduce the numbers of such votes. Evaluative Proportional Representation not only wastes no votes quantitatively, it also claims to remove the needless qualitative wasting of votes. Each EPR voter is invited to grade each of the candidate's suitability for office as either Excellent (ideal), Very Good, Good, Acceptable, Poor, or Reject (entirely unsuitable). Each citizen is assured that their one vote will proportionately increase the voting power of the elected member of the legislature who received either their highest grade, remaining highest grade, or proxy vote.

The term may be considered pejorative by opponents of such systems. Their arguments may either suggest that in any voting system each vote is wasted (unless the result is decided by a single vote), or that no vote is wasted as each one sends a political signal which will be taken into account in preparation for the subsequent election.

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. In some electoral systems, it may be plausible for less-popular candidates to make similar appeals to supporters of more-popular candidates. In a plurality voting system, the term "wasted vote" is not usually applied to votes for the second-placed candidate, but rather to votes for candidates finishing third or lower. This is a reflection of Duverger's Law, i.e. the institutionalisation of a two-party system.

## Example calculations of wasted votes

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 and is therefore elected. The wasted votes are:

• All 3801 votes for candidates B and C, since these did not elect any candidate
• In the wider definition, 2899 of the 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 12 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 only with 2800 votes would B lose the last seat to C.

A majority of votes are always wasted (in the wider sense) in a single-seat election, unless there are exactly two candidates and the margin of victory is exactly one vote. Multi-seat constituencies reduce the number of wasted votes as long as proportional representation is used. (When used with winner-take-all systems, as with the US Electoral College, multi-member constituencies may see the wasted vote reach or exceed 50%).

## Efficiency gap

Wasted votes are the basis for computing the efficiency gap, a measure devised by University of Chicago law professor Nicholas Stephanopoulos and political scientist Eric McGhee in 2014. This statistic has been used to quantitatively assess the effect of gerrymandering, the assigning of voters to electoral districts in such a way as to increase the number of districts won by one political party at the expense of another. The heart of the computation is to add up, over all electoral districts, the wasted votes of each party's candidates. The efficiency gap is the difference between the two parties' wasted votes, divided by the total number of votes.[1][4] Stephanopoulos and McGhee argued that in a non-partisan redistricting with two roughly equally popular parties, the efficiency gap would be zero, with an equal number of wasted votes from either party. If the gap exceeded 7%, then Stephanopoulos and McGhee argued that this could ensure the party with fewer wasted votes would be able to control the state for the duration of the validity of the district map.[5][6]

Citing in part an efficiency gap of 11.69% to 13% in favor of the Republicans, a U.S. District Court ruling in Whitford v. Gill in 2016 ruled against the 2011 drawing of Wisconsin legislative districts. It was the first U.S. Federal court ruling to strike down a redistricting on the grounds of favoring a political party. In the 2012 election for the state legislature, Republican candidates had 48.6% of the two-party votes but won 61% of the 99 districts. The court found that the disparate treatment of Democratic and Republican voters violated the 1st and 14th amendments to the US Constitution.[7] The State has challenged the District Court's ruling, and in June 2017, the Supreme Court has agreed to hear arguments in this case. The state is expected to challenge the validity of the efficiency gap measure.[5]

### Sample calculation

The following example illustrates the efficiency gap calculation.[4] There are two parties, A and B. According to the original paper,[1] wasted votes for the winner (say A) are those "beyond the 50 per-cent threshold needed" i.e., beyond 50% plus one or A-((A+B)/2+1) or more simply (A-B)/2-1, if A-B is even, like here, otherwise use int((A-B)/2). There are 500 voters divided into 5 districts with 100 voters each. In the recent election, Party A had about 45% of the votes but won 4 of the 5 districts, as follows:

1 53 47 A 2 47
2 53 47 A 2 47
3 53 47 A 2 47
4 53 47 A 2 47
5 15 85 B 15 34
total 227 273 4-A, 1-B 23 222

The efficiency gap is the difference in the two party's wasted votes, divided by the total number of votes.

• All votes for a losing candidate are wasted .
• To win a district, 51 votes are needed, so the excess votes for the winner are wasted votes.

Efficiency gap = ${\displaystyle {\frac {222-23}{500}}=39.8\%}$  in favor of Party A.

Party A has less than half the votes, but far more of Party B's votes are wasted.

### Shortcomings

The Efficiency Gap (EG) measure has been shown to have a number of shortcomings.[8] Most notably, it largely reduces to a simple measure of the relationship between the statewide vote lean minus half the seat lean. A state with 60% of its residents belonging to a single party and an election that awarded 60% of the seats to that party—in other words, a perfectly proportional outcome—would therefore be labeled as problematic vote, because its Efficiency Gap would be ${\displaystyle 20\%-10\%=10\%}$ , higher than the 8% often cited as a threshold for evidence of gerrymandering.(see Note) This shows EG, powerful as it can be, is insufficient, by itself, for guaranteeing lack of gerrymandering, which guarantee, if it exists, requires additional measures, like compactness measure of a shape as evinced in examples from the paper, which concludes

The Wisconsin plaintiffs are not asking the court to enshrine EG as the one true measure of partisan gerrymandering, but only to accept it as a starting point in building a test to show when entrenched partisan advantage has risen to the level of vote dilution of political opponents. We hope that the Supreme Court agrees with them in a decision that leaves room for EG to pave the way for reﬁned metrics and methods in the years to come.[8]

Note, normalizing EG to a particular proportional split in the population may correct this. One possible Corrected EG (CEG) is (1(+or-)EG)/(1+IEG) -1, where IEG is EG for the ideally proportioned case, as above. The sign used with EG depends on whether the wasted votes favor the majority party(+) or not(-). CEG = 0% for the ideally proportioned case, and CEG = 0.9/1.1 -1 = -18.18% for the reverse case of the above, 10% EG against the majority party. North Carolina is a gerrymandered state[9] with previously 3 Democrats registered for every 2 Republicans (~60/40 as above) but elects only 3 Democrat vs 10 Republican Congressmen. [10] The NC CEG for 2016 is (1-0.1928)/1.1 -1 = -26.62%, and for 2018 is (1-0.2746)/1.1 -1 = -34.05%. EGs here are negative for the majority party wasted vote disadvantage. Reject an hypothesis of no gerrymander if |CEG| > something like 10%.