Equally Weighted Vote

An Equally Weighted Vote is the concept that every vote should carry equal power or weight. In 1964, Wesberry v. Sanders, The U.S. Supreme Court declared that equality of voting - one person, one vote - means that "the weight and worth of the citizens' votes as nearly as is practicable must be the same."

Votes can be unequally weighted at a number of different stages in the election process. First, a vote can be unequal due to the voting method itself. Any voting method which allows Vote Splitting ensures that voters do not have an equally weighted vote in elections which have more than two candidates. Second, votes for representatives to a larger geographical area who are representing a district within that area can be unequally weighted due to district lines which may bias an election in favor of one faction or another. When district lines are intentionally drawn in order to marginalize specific factions, (reducing the weight of those voters relative to others) it's known as Gerrymandering.

The Electoral College and other mechanisms which use representatives to determine elections rather than directly using the votes cast also violate the Equally Weighted Vote, particularly in cases where electors or representatives are not allocated proportionately to the population. In the case of the Electoral College each state is awarded electors based on the number of members of congress. The House of Representatives is based on population, which would ensure that electoral votes were equally weighted as nearly as is practicable, but each state is also awarded two additional electors per state corresponding to their two Senators. This results in US presidential elections which specifically violate the Equal Vote Criterion.

The 1964, Wesberry v. Sanderscase cited above addressed Gerrymandering. In the case of district lines it's impossible to ensure that elections will not favor one faction or the other over time as populations grow and change, but it is "practicable" to prevent and mitigate this phenomena. However in the case of vote splitting and the Electoral Collage achieving a perfectly Equally Weighted Vote is fully possible.

Equality Criterion
Otherwise known as the Equal Vote Criterion. Any single-winner or multi-winner bloc voting method which passes the Test of Balance passes the Equality Criterion and can be said to guarantee an Equally Weighted Vote. In order for a voting method to pass the test of balance the ballot must allow voters to give equal support to candidates, and there must be no limit as to the number of candidates who a voter can support.

The Test of Balance
The Test of Balance is defined as the following: "A voting method definitively provides votes of equal weight to all the voters if, and only if, for each possible vote expression that one voter may cast in an election, there exists another expression of the vote that another voter can cast that is in balance, such that the outcome of the election is the same whether both or neither votes are counted." In short, "Any way I vote, you should be able to vote in an equal and opposite fashion." - Mark Frohnmeyer, founder of the Equal Vote Coalition.

Voting methods which ensure an Equally Weighted Vote
Voting Methods which ensure an Equally Weighted Vote with any number of candidates include Approval Voting, Score Voting, STAR Voting, as well as a number of others. In general Cardinal Voting methods ensure an Equally Weighted Vote for each voter. Many Condorcet methods (most that can be calculated only with the pairwise counting matrix, most Condorcet-cardinal hybrids, etc.) also pass the criterion.

Choose One Plurality Voting does not satisfy the Equal Vote Criterion. Instant Runoff Voting (often referred to as Ranked Choice Voting) does not satisfy the Equality Criterion. Any voting method will satisfy the Equality Criterion in elections with two candidates only.

Vote unitarity
One application of the Equally Weighted Vote in the context of proportional representation is vote unitarity. The basic idea is that the vote should stay equally weighted or reweighted throughout the election tabulation. A voter's influence on electing subsequent winners should directly depend on the amount of support given to prior winners. This means that an individual voter's vote weight is conserved throughout the process.

There is an important nuance to this with regards to Surplus Handling; if, say, every voter gives one of the winners a top score, then instead of everyone's vote having no influence on the other winners, 'proportionate spending' ensures a proportionate decrease in voting power, to ensure that the cost to elect a candidate is consistent, and to ensure that every voter still has a the correct amount of influence on the remaining winners. The simplest implementation of this is with Sequentially Spent Score.

In summary, there is a proportional relationship between how much support the voters give to the winners, the cost to elect a winner, and the amount of influence that is removed from the voters, to ensure that every voter has a chance to fairly elect someone they prefer. The prominent Single Transferable Vote, and Reweighted Range Voting methods fail vote unitarity.