Voting Rules for

Different uses for voting need different types of voting.

Notes & Quotes Evolving toward stability, Sabbatical terms

Seats and Rules

Shares A brief history of quotas, the votes needed for victory
Major parties or coalitions rarely win over 60% of the PR seats. That share must be reduced by 1 out of 6 to become less than 50%, preventing the group from forming an off-center majority. So at least one-sixth of the seats should be filled by Condorcet's rule.

Voters in some districts tend to be liberals (or conservatives) so some single-winner seats will be won by supporters of the largest PR party. It is therefore better to elect more than one-sixth of the seats by Condorcet's rule. A 100 seat council might have 70 to 80 reps elected by list PR and 20 to 30 from single-winner districts using Condorcet's rule. A party then needs about 1.25% of the votes to win 1 PR seat, 64% for 51 seats.

The most common split is half and half: 50% of the seats for reps from single-winner districts and 50% from PR party-lists. But the districts use plurality rule and so elect reps from major off-center parties that routinely refuse to work with each other. Using Condorcet's rule to fill half of the seats might give too much weight to the center.

Voting rules must be adapted to organizational cultures. Small councils have to make tradeoffs, deciding which qualities are most needed: electoral competition, minority representation, or policy moderation.

In deciding the voting rule and number of seats for a council, consider the shares of votes for current interest groups. A group with 17% of the population could more likely win 1 of 5 PR seats than 1 of 4. So that district might elect a council of 5 by LERa rather than by LERb. (Better yet, expand the council.) The framers of a charter or constitution may find simulations of current factional voting and a variety of rules helpful in finding the best rule for their needs.

For LER to work well, there must be as many neutral voters as the difference in size between the polarized factions. LER can help only a little in a jurisdiction so unevenly polarized that the median voter is in 1 pole. In that case, the most LER can do is give the chair to a moderate member of the dominant pole.

A dominant majority can win control of a council under any fair election rule. Minorities in that case need the protection of the courts. Yet LER can help some: Condorcet's rule gives minority voters some say on which majority candidate becomes the chairperson and STV gives them their own voice on the council. (New voting rules for setting budgets can give minorities limited shares of spending power.)

To ensure the council's chairperson is central to all the voters, she should be elected directly by the voters using Condorcet's rule. She should not be elected by the council. Otherwise the biggest faction of reps would elect someone near the center of their coallition. And she should not have the power to veto legislation, only her power as a symbol and a swing vote.

The roles for the lone chairperson and the various reps differ significantly. They have different constituencies: the chair's is the whole electorate, each rep's is a narrower interest group. Their election rules should heed those constituencies.

9-seat councils should include 2 Condorcet-series Winners. The first winner is the chairperson; the second competes to define the best-balanced policies -- in hopes of winning the chair next time. The 3 or 4 liberals will compete with each other for liberal voters and the 3 or 4 conservatives will do likewise. This also allows inter-party competition for swing PR seats.

The reps may form inner (moderate) and outer (radical) rings around the center if party discipline does not force them to cluster. The chair may build majorities with the inner circle of moderate reps.

The LERab rule exempts 1 Condorcet winner from elimination (as in LERa) and elects a second Condorcet winner at no charge to voters' weights (as in LERb). LERbb would give a majority party or coalition 2 extra seats, much more than its proportional representation. So fill only 1 seat with no charge. LERaa with 2 Condorcet winners immune from elimination, would restrain the weights of many ballot's from electing more favored candidates. So hold only 1 candidate immune from elimination.

Separate races for 7 STV seats plus 2 Condorcet winners have advantages: Shorter lists make voting easier on the STV ballot. And the candidates for chair identify themselves clearly. But this system would give a majority coalition 2 extra seats, much more than its fair share of representation.

Many groups use overlapping terms. They could alternate 4- and 5-seat elections. Each would divide the electorate differently. So the winners could represent different sectors of the community. The council might be more diverse than a pair of 5-seat elections. But not as diverse as a 9-seat election.

7-seat councils could use LERab and 2 Condorcet winners. But they might often form a majority with the moderate STV winners -- giving too much power to the center and not forming an inclusive nor balanced majority.

Seven is the usual size for "action-taking groups" according to research cited by Mancur Olson in The Logic of Collective Action. These include sub-committees of corporate boards and of state and national legislatures. Larger councils are often used for information gathering. For example, some councils rely on face to face communication with constituents in geographic units such as barrios or homerooms. For that they often use a large number of reps from single-winner districts. They can also elect a diverse executive council of 5 or 7 to lead the larger legislative council.

5-seat councils are the smallest that can represent a community which has 3 kinds of issues, not only left versus right but a 3D "issue space". (The second dimension is often authoritarian versus democratic.) LERa tends to elect a chairperson at the center and 4 reps near the corners of a 3D pyramid. The chair may ally with 1 moderate from each side of an issue to make a balanced majority. In practice, 5-seat PR districts "waste" fewer votes than 3-seat districts, that means fewer votes go to parties that fail to win a seat and each party's share of seats is much closer to its share of votes.

3-seat councils that use consensus may find STV the best election rule because it might represent a greater number of interest groups and range of opinions than LERa. But when a board votes on some decisions, the 2 rep majority would tend to leave out the third rep's point of view.

LERa is better here; its chairperson tries to center and balance each policy. She participates in the discussion, explains the option she prefers and asks the reps to move closer to it. The winner is the 1 who moves closest to the chair's balanced view. This is not a 1-sided victory. It gives only slightly more to 1 side than to the other. A chairperson who makes bad compromises may be replaced at the next election.

When reps are chosen for their philosophies and not for specific skills, the council may need to rely on a skilled and impartial staff.

(Some LERa simulations end with a fringe candidate and the Condorcet winner, who may not be eliminated, competing for the last seat. The fringe candidate is eliminated and her supporters' weights transfer to the center. If the last candidate eliminated has more votes than the Condorcet winner, LORa suggests changing the rule to LERb. Rare LER or STV simulations show some weights transferring even farther, all the way from 1 side to the other.)

5  	  7	Seats
100	100	Voters
 16.67	 12.5	Droop quota for chair
 83.33	 87.5	Votes left for reps
 20.83	 14.58	Hare quota for reps
 68	 63	Majority ballots
 32	 37	minority ballots
20.83	29.17	minority ballots used for 1 [2] reps
 11.17	 7.83	minority votes left
 58.33	56.25	Majority ballots for chair + 2 [3] reps
  9.67	 6.75	Majority votes left
TRUE	TRUE	minority wins last seat. 

Here is a decision tree for selecting voting and quota rules.

I) How many people will be elected ?
A) Single-Winner Election: Pick a chairperson or president.
B) Multi-Winner Election: Fill a sub-committee or legislature.
(Rules for setting policies, budgets, and projects are explained on later web pages.)

A) Select a chairperson, mayor, or president.
Can the winner veto legislation ?
If so, use IRV, otherwise choose a Condorcet rule:
Is strategic voting rewarded?
If it is, break Condorcet ties (voting cycles) with Schulze's Beat Path, Tideman's Ranked Pairs, or IRV (see Hill), otherwise use Borda, Dodgson or Minimax. The latter three are more likely to elect the “utility maximizing candidate.”

B1) Fill a board of directors, sub-committee, or legislature.
Is this an inclusive or exclusive organization ? (Recall the two views on electing reps.)
If it is exclusive, use Tideman's Ranked Pairs rule for a multi-winner Condorcet Series. If the council is inclusive, select an ensemble rule below.

B2) Ensemble Rules
1) Does the council have more than 9 seats ?
If so divide voters into several voting districts and continue the key below,
or fill 20% to 30% of seats from Condorcet districts, the rest by open-list PR.
2) Does the council have 9 seats ?
If so use LERab defined above or fill 7 seats by STV and 2 by Condorcet.
If not use LERa with Droop quota for the chairperson and simple quota for other seats.

[ Optional: B3) If LERa found the last candidate eliminated had more firsts than the chairperson did at that time:
Does the district have more than 3 seats ?
If so, use LERb and simple quota.
If not use STV with Droop quota.]

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