# Electoral System Glossary

Voting theory comes with lots of jargon and unfamiliar terms. You can find all the terms you need to know right here.

## Electoral System Terms Defined

- Bloc
A bloc method is a multi-winner voting method classification. It’s the opposite of proportional. Under this method, if a “bloc” of voters greater than 50% all vote the same way, then that bloc can determine all the seats.

- Cardinal
A cardinal method is any voting method that allows voters to score their choices along a scale of at least two units. Voters may give equal scores to different choices.

- Closed Partisan Primary
A closed partisan primary is a primary where voters must choose within the party in which the voter is registered. Each party advances the candidate within its party that was chosen the most.

- Multi-Winner
A multi-winner method is any voting method that selects more than one winner.

- Nonpartisan Primary
A nonpartisan primary is a primary where a determined number of candidates move onto the general election without regard to political party. Nonpartisan primaries are always open so that all voters voters may choose among all the candidates regardless of party.

- Open Partisan Primary/ Partisan Blanket Primary
An open partisan primary is a primary where voters may choose within the the one party of their choosing regardless of the voter’s own party affiliation. Each party advances the candidate within its party that was chosen the most. Note: This type of primary was determined to be unconstitutional in the US; See: California Democratic Party v. Jones.

- Parliamentary System
A parliamentary system means that the governing body, a parliament, elects its prime minister. This is as opposed to the public electing a president. A parliamentary system is unrelated to whether the voting method used is proportional.

- Partisan Primary
A partisan primary is a primary where each political party receives a nominee that moves to the general election.

- Plurality-Based
A plurality-based voting method is a voting method that utilizes plurality voting.

- Preferential
A preferential voting method is any voting method that allows voters to rank at least two choices. These methods typically require voters to not rank any choice equally.

- Primary
A primary is a preliminary election used to narrow down the candidate pool for a later round. The later round is called the general election.

- Proportional
A proportional voting method is a multi-winner voting method classification. It gives outcomes that are proportionately responsive to the selections that voters give. For example, if a 30% bloc of voters supports an ideology, then roughly 30% of the winners will have that ideology.

- Semi-Open/Semi-Closed Partisan Primary
A semi-open/semi-closed partisan primary is a primary where voters may choose within one party of the voter’s choosing but only if the party allows them. Any party may choose to limit voters to vote within their party only if they are registered, or the party may choose to allow voters registered under another party or no party to vote within their party. Each party advances the candidate within its party that was chosen the most.

- Semi-Proportional
A semi-proportional method is a multi-winner voting method classification. It gives outcomes between bloc and proportional. Semi-proportional methods tend to be more proportional as the number of winners increases.

- Single-Winner
A single-winner method is any voting method that selects one winner. Some political positions are inherently single-winner like mayor, governor, or president.

- Top-Two Primary/Jungle Primary/ Louisiana Primary/ Cajun Primary/ Nonpartisan Blanket Primary
A top-two primary is a primary where voters may choose any one candidate, regardless of party. The top two candidates selected the most, regardless of party, move onto the general election. Some top-two primaries declare a winner immediately if a candidate receives greater than 50% of the primary vote.

- Winner-Take-All
A winner-take-all election chooses just one winner. In practice, winner-take-all elections typically refer to positions that could be conducted as a multi-winner election. But instead the elections are conducted as a single-winner election where the candidates are associated with a smaller geography. This decision to use a winner-take-all election rules out the ability to use a proportional or semi-proportional method.

## Voting Methods Defined

- Approval Voting (Single-Winner)
### EXPRESSION

Each voter chooses (no ranking) as many candidates as desired. Voters may not vote more than once for any one candidate.

### CALCULATION

Add all the votes. The candidate with the most votes wins.

- Bloc Approval Voting (Multi-Winner)
### EXPRESSION

Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate.

### CALCULATION

Add all the votes. Elect the candidates with the most votes until all positions are filled.

- Asset Voting (Multi-Winner)
### EXPRESSION

Each voter chooses one candidate.

### CALCULATION

Add all the votes. All the candidates will have a specified time limit to trade their votes amongst themselves. Negotiations are expected. Elect the candidates with the most votes until all positions are filled.

- Bloc Plurality Voting (Multi-Winner)
### EXPRESSION

Each voter chooses as many candidates as there are seats to be elected.

### CALCULATION

Add all the votes. Elect the candidates with the most votes until all positions are filled.

- Bloc Score Voting (Multi-Winner)
### EXPRESSION

Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable.

### CALCULATION

Add all the votes. Elect the candidates with the highest scores until all positions are filled.

- Borda Count (Single-Winner)
### EXPRESSION

Each voter ranks their choices from first to last.

### CALCULATION

Assign each ranking its value. A first choice is assigned one less point than there are choices. A last-ranked choice gets zero points. Sum these points for each candidate. Elect the candidate with the most points.

- Bucklin Voting (Single-Winner)
### EXPRESSION

Each voter ranks their choices from first to last.

### CALCULATION

Total all first-choice votes. If a candidate has greater than half these votes among the valid ballots, then elect that candidate. If not, the second choice votes are added to the candidates’ totals. Repeat adding in the lower-choice votes until a candidate has greater than half the total votes among the valid ballots. If multiple candidates have at least half the total votes, then elect the one with the most votes.

- Closed Party List (Multi-winner)
### EXPRESSION

Each voter chooses one party.

### CALCULATION

Sum the votes for each party. Give the first seat to the party with the most votes. Parties choose the order their candidates are elected. The ballots are reweighted by whether they selected a winner. This reweighting is done after each seat is filled by an algorithm (ex// Sainte-Laguë, d’Hondt). Continue to elect candidates and reweight the ballots each time until all the seats are filled.

- Condorcet Voting (Single-Winner)
### EXPRESSION

Each voter ranks their choices from first to last.

### CALCULATION

Use the rankings to create head-to-head (pairwise) comparisons for all the candidates. This is just like a round-robin tournament. Elect the candidate that wins all the head-to-head comparisons with every other candidate. It is possible for this Condorcet winner not to exist (i.e. a cycle/ Condorcet Paradox). When a Condorcet winner doesn’t exist, different Condorcet methods use different (often complex) tie-breaker techniques (Ex// Schulze, Ranked Pairs).

- Cumulative Voting (Multi-Winner)
### EXPRESSION

Voters are given as many votes as there are positions elected. Voters may place these votes on any number of candidates. Voters can place multiple votes on the same candidate.

### CALCULATION

Elect the candidates with the most votes until all the positions are filled.

- Instant Runoff Voting/Ranked Choice Voting/Alternative Vote/Hare (Single-Winner)
### EXPRESSION

Each voter ranks their choices from first to last. The number of rankings allowed may be limited to three in some cases.

### CALCULATION

Total all the first-choice votes. If a candidate has greater than half these votes among the valid ballots, then elect that candidate. If not, then eliminate the candidate with the least first-choice votes. Look at the ballots from that eliminated candidate. Transfer that candidate’ next-choice votes to those candidates and treat those votes as first-choice votes. Again, look to see if a candidate has greater than half these first-choice votes among the valid ballots. If there is again no winner, then repeat this process until a candidate has greater than half the total votes among the remaining valid ballots.

- Limited Voting (Multi-Winner)
### EXPRESSION

Each voter chooses a number of candidates less than are being elected. This exact number of votes is determined ahead of time by the electoral engineer. Voters cannot place more than one vote on any candidate.

### CALCULATION

Elect the candidates with the most votes until all the positions are filled.

- Majority Judgement (Single-Winner)
### EXPRESSION

Each voter chooses an ordinal grade for each candidate (Ex// Excellent, poor, A, F).

### CALCULATION

Order the candidates’ votes from best to worst. Determine the median grade for each candidate. Elect the candidate with the highest median grade. If multiple candidates share the highest median grade, a tie-breaking procedure is applied.

- Open Party List (Multi-Winner)
### EXPRESSION

Each voter chooses a party or the independent category. The voter then selects a candidate within their chosen party/independent category.

### CALCULATION

Add the votes for each party or independent category. Have the party or independent category with the most votes gets the first seat. Elect the candidate within that selection via Single Non-Transferrable Vote. Reweight the ballots after each candidate election by whether it selected a winner. Use a predetermined algorithm for this reweighting (ex// Sainte-Laguë, d’Hondt). Continue to elect candidates and reweight the ballots each time until all the seats are filled.

- Plurality Voting/First-Past-the-Post (Single-Winner)
### EXPRESSION

Each voter chooses only one candidate.

### CALCULATION

Add all the votes. Elect the candidate with the most votes.

- Plurality Voting with Runoff (Single-Winner)
### EXPRESSION

Each voter chooses only one candidate in the first round. In the second round, each voter chooses one of two candidates.

### CALCULATION

Add all the first-round votes. Advance only the two candidates with the most votes to the second round (runoff). For the second round, add up all the votes for the two candidates. Elect the candidate of the two with the most votes.

- Proportional Approval Voting (Multi-Winner)
### EXPRESSION

Each voter chooses (no ranking) as many candidates as desired. Voters may not vote more than once for any one candidate.

### CALCULATION

Add all the votes. Elect the candidate with the most votes in the first round. After each round, use the following formula to reweight the ballots: (1/ (1 + Total Approvals Given to Elected Candidates)). Continue to elect candidates and reweight the ballots each time until all the seats are filled.

- Reweighted Score Voting (Multi-Winner)
### EXPRESSION

Each voter chooses (no ranking) as many candidates as desired. Voters may not vote more than once for any one candidate.

### CALCULATION

Add all the votes. Elect the candidate with the most votes in the first round. After each round, use the following formula to reweight the ballots: (1/ (1 + Total Approvals Given to Elected Candidates)). Continue to elect candidates and reweight the ballots each time until all the seats are filled.

- Score Voting/Range Voting
### EXPRESSION

Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable.

### CALCULATION

Add all the scores. Elect the candidate with the highest score.

- Single Transferable Vote/Choice Voting
### EXPRESSION

Each voter ranks their choices from first to last.

### CALCULATION

Add all the first choice votes. Typically, the Droop Quota is used: (Total Current Valid Votes/ (Total Seats to Fill + 1)) +1. This quota determines the number of votes needed to elect a candidate for a given round. If a candidate meets this quota with enough first-choice votes, then elect that candidate. Transfer the surplus votes that went above the quota to those ballots’ next ranked candidate. This procedure may use exact fractions to consider the surplus’ size. It may also use other procedures such as random transfers. Continue until you elect all the seats or no candidate meets the threshold. If seats still must be filled and no candidate meets the threshold, then look to the candidate with the least number of first-choice votes. Eliminate that candidate. Transfer all the ballots from that candidate to those ballots’ next ranked candidate. Repeat until another candidate meets the quota. Then repeat this process until all the seats have been filled.

- Single Non-Transferable Vote
### EXPRESSION

Each voter chooses only one candidate.

### CALCULATION

Add all the votes. Elect the candidates with the most votes until all positions are filled.

## Evaluative Terms Defined

- Bayesian Regret
Bayesian regret is a utility value output produced through simulated elections. This approach creates a quantitative measure of voter satisfaction while comparing different voting methods. The simulation allows simultaneous interactions of other variables such as tactical voting, voter ignorance, and number of issues.

- Condorcet Criterion
The Condorcet criterion is satisfied if when a candidate can beat every other candidate in a head-to-head election, that beat-all candidate always wins.

- Criterion
A voting method criterion refers to whether a voting method can behave in a certain undesirable way. If the method can’t ever behave in the undesirable way, then it is said to pass that criterion. But if it can behave in the undesirable way in any circumstance, then the method fails that criterion. This failure is recognized regardless of the undesirable behavior’s degree or frequency.

- Favorite Betrayal Criterion
The favorite betrayal criterion is satisfied if a voter’s ballot always benefits by showing the greatest support for a favorite candidate.

- Independence of Clones Criterion
The independence of clones criterion is satisfied if an otherwise winning candidate is not caused to lose by introducing an identical candidate.

- Independence of Irrelevant Alternatives Criterion (IIA)
IIA is satisfied if adding an additional non-winning candidate can never change the winner.

- Later-No-Harm Criterion
The later-no-harm criterion is satisfied if a voter cannot cause a more preferred candidate to lose by giving an additional ranking or positive rating to a less preferred candidate.

- Majority Criterion
The majority criterion is satisfied if when more than half of voters prefer a candidate, that (absolute) majority candidate always wins.

- Monotonicity Criterion
The monotonicity criterion is satisfied if (1) giving greater support for a candidate can never hurt that candidate, and (2) giving less support for a candidate can never benefit that candidate.

- Weak Majority Criterion
The majority criterion is satisfied if when more than half of voters prefer a candidate, voters can always strategically vote so that (absolute) majority candidate wins.