Three-round system

The three-round system (3RS), also known as primary-runoff co-voting or third ballot, is a voting method used to elect a single candidate out of an unspecified number of candidates. It is a synthesis of the two-round system and the primary election.

History

TBA

System

First round

The first round, also called the "primary election" is the first round in the election. Voters are presented with a ballot including all candidates running for the election. This round serves as a basic filter for candidates, testing if they can garner enough support to run for the election and not just split votes of more perspective candidates.

In this round, voters elect the candidates they wish to run using approval voting, giving their vote to an unspecified number of candidates they wish to run in the second round. A candidate continues into the second round if they meet at least one of the three following conditions:

1. Appear at least 20% of all ballots
2. Get at least 10% of all votes
3. Get an exclusive support (they recieve the only vote on a ballot) on at least 5% of all ballots

A candidate can be elected if they appear at least 75% of all ballots and the second highest ranked candidate hasn't appeared on 60% or more of all ballots.

If there are only two candidates who managed to meet the quorum on candidacy, the second round is skipped and the elections happen only between those two most successful candidates using the third round rules.

If only one or no candidate managed to meet the quorum for continuous candidacy, the two highest ranking continue to the third round, with the second round being skipped.

Second round

In the second round, the voters choose between all candidates who managed to meet at least one of the three conditions of the first round. Voters elect the candidates using cumulative voting, where the voter can either give two votes to a single candidate or split their votes between two candidates.

This system, in contrast to the standard two-round system, ensures, that if a voter is split between two candidates, they can give their vote to both candidates. Two voters split between two candidates who both give one vote to either of the two candidates ensure that both of those candidates recieve the same number of votes as a single candidate who recieved an exclusive vote by a single voter.

Two most successful candidates continue to the third round of voting, unless a single candidate recieves at least 50% of all votes, where they are elected outright without a runoff. If there is a tie on the second place, the number of exclusive votes is checked and the candidate with a smaller number of exclusive votes continues into the second round. If even after this control and an ordered recount, the tie prevails even in the number of exclusive votes, the third round is expanded to accomodate all the tied candidates.

Third round

In the third round, the voters choose between two remaining candidates using plurality voting. The candidate with at least 50% of the votes wins. If there are more than two candidates due to a tie in the second round and no single one reaches 50%, the two most successful candidates continue to a parliamentary runoff. If there is a tie on the second place, the parliamentary runoff is expanded to accomodate all the tied candidates.

Parliamentary runoff

In the parliamentary runoff, the parliament, local assembly or a specifically assembled electoral college (depending on the type of the election) serve as a tiebreaker to pick the final candidate. If a tie in voting still occurs, the vote repeats until a single candidate is elected.

Example

Eight candidates, labelled as candidates A-H, run for a presidential election.

Candidate		% of ballots	% of votes	% of exclusive votes	Continue to round 2?	Chart
	CANDIDATE A	48.0%	16.8%	1.2%	Yes	% of votes
	CANDIDATE B	14.9%	5.2%	0.3%	No
	CANDIDATE C	20.9%	7.3%	0.1%	Yes
	CANDIDATE D	77.3%	32.3%	0.5%	Yes
	CANDIDATE E	12.0%	4.2%	3.8%	No
	CANDIDATE F	66.3%	26.7%	0.8%	Yes
	CANDIDATE G	11.3%	3.8%	1%	No
	CANDIDATE H	7.3%	3.1%	6.1%	Yes
Invalid		—	0.6%	—	—
Quorum		20%	10%	5%	—	Round 1

Out of those eight, five continue to round two:

Candidate		% of votes	Continue to round 3?	Chart
	CANDIDATE A	28.7%	Yes	% of votes
	CANDIDATE C	14.7%	No
	CANDIDATE D	31.5%	Yes
	CANDIDATE F	17.7%	No
	CANDIDATE H	6.7%	No
Invalid		0.7%	—
Quorum		Top 2	—	Round 2

Out of those five, two continue to round three:

Candidate		% of votes	Elected?	Chart
	CANDIDATE A	56.8%	Yes	% of votes
	CANDIDATE D	42.7%	No
Invalid		0.5%	—
Quorum		50%	—	Round 3

Usage

Three-round system is used in multiple countries across the world, most commonly to elect a head of state. This system is currently employed by:

• Zhousheng for the president