Majority Rule

The idea of majority rule is simple:

• Let a decision be supported by at least a majority (50%+1)

There's nothing special about 50%+1, except that it is the highest guaranteed support in an either/or question with definitive results. (There's just one case of failure - an exact split on an even number of votes - traditionally broken by a coin toss or cutting a deck of cards.)

You can also consider decision by a "super majority": Let a decision be supported by at least 60%. It's an equally valid requirement, but much less practical if a decision MUST be made immediately.

However even a 50%+1 rule STILL fails when voters are given more than two choices.

Consider the 1998 Minnesota Governor race:
http://www.sos.state.mn.us/election/genstate.pdf
**********************
RP, VENTURA 37.0%
R, COLEMAN 34.3%
DFL, HUMPHREY 28.1%
GPM, KEN PENTEL 0.3%
LIB, GERMANN 0.1%
GRP, WRIGHT 0.1%
**********************

In a 3-way race, everyone having one vote, no choice was supported by 50%.

Our partisan elections work by "Plurality" which means "Most votes win".

A plurality system offers no lower limit for support by winners. It can allow a candidate who is supported by a majority head-to-head over every other candidate to lose because voters had too many choices and another candidate can win merely for being MOST DIFFERENT from the other candidates.

We can do better and there's a number of competing systems that could allow us to pick our winners by AT LEAST 50%+1 of the voters.

1) Top-two Primary

http://www.seattleweekly.com/features/0448/041201_news_primary_primer.php
http://www.fairvote.org/irv/louisiana.htm

This system is what many cities do for mayor with nonpartisan elections. The primary allows everyone a chance to support their favorite, and the strongest two candidates go forward to the general election.

We don't have this option within Partisan elections because the primary is used to pick the top candidate within each party.

2) Top-two Party Primary

This system is a hybrid between a "top-two primary" and a "Partisan primary"

A Partisan primary allows the top candidate from each party to advance to the general election.

This hybrid system combines the votes for all the candidates in a single party, and the two parties with the most combined votes get ONE candidate to advance to the general election.

This system is BETTER than a "partisan primary" because there's open competition between all candidates. Voters are free to choose their favorite candidate from different parties among different elections. I might vote for a Republican for Governor, a DFL for Attorney General, and a Libertian for Secretrary of State. There's no threat of insincere "cross-over" voting because every party is at risk of elimination and no one can risk voting for a candidate besides their favorite.

So again, the general election is down to the strongest two candidates and one will get a majority.

3) December top-two runoff or (Two Round System)

http://www.aceproject.org/main/english/es/esd04.htm

If no candidate has a majority in the November election, the top-two candidates can be retained in a runoff election in December. This approach is used in a number of states. (Some only hold the runoff if no candidate exceeds 40% of the vote)

This again allows a majority decision, but requires voters to come out again to vote and often causes reduced voter turnout, and requires more money for ballots and counting. Still, it is a valid method, giving the voters a final chance for a majority to unite behind one candidate.

4) Instant Runoff Voting (IRV) - http://www.fairvote.org/irv/

This system allows voters to offer rank preference choices. For example: 1) Ventura, 2) Pentel, 3) Coleman. First choice votes are tallied. If no choice has a majority, the weakest candidates are eliminated, and votes for eliminated candidates are transfered to a next choice - just like a real runoff. There's no fear in offering lower preferences because they only count if all higher preferences are eliminated.

When there's only two candidates remaining, one will have a majority support.

There are variations on IRV. The standard model says to eliminate one candidate at a time. A quicker system follows the top-two approach, eliminating all but the top two candidates in the first round. The primary difference is a slower runoff allows the chance for an initially third place candidate a chance to rise up and win, while a top-two runoff disallows that.

The primary issue with IRV would be in voter education (marking ballots) AND higher demands on voters. In order for your vote to count, you have to offer enough preferences until you're sure one of them will make the final top-two. If you fail to rank enough choices, your vote will become wasted - just like if you didn't vote in the last runoff round.

5) Condorcet pairwise system - http://www.eskimo.com/~robla/politics/condorcet.html

The primary problem with runoffs in general is in a close 3-way race, any candidate might win depending which two survives to the final round.

If you have an election like : Coleman=38%, Humphrey=31.01%, Ventura=30.99% . Anything close to a tie means a small shift in votes would change the final two candidates, and possibly the final winner.

How do you fairly eliminate one of these three? The Condorcet method says don't eliminate any of them and instead compare them in pairwise elections:

Pretend Head-to-Head comparisons:
Ventura beats Coleman 51% to 49%
Ventura beats Humphrey 55% to 45%

Given these example result above, we can see Ventura is the strongest candidate and deserves to win. It doesn't matter weather Coleman beats Humphrey or vice versa because Ventura can beat both of them.

This is the approach of the Condorcet method. Such a winner is called "Condorcet's winner".

NOTE: When I give these head-to-head "subelections", they are assumed to be measured from rank-preference ballots, like IRV. Everybody's vote counts between each pair once. (Voters do not need to rank all the candidates, but obviously benefit in ranking all acceptable candidates who stand a chance of winning.)

A theoretical drawback of this approach is that it is possible no candidate will meet this condition. For example in the rock-paper-scissors game, there's a cycle of head-to-head wins - the balance of power excludes a "center" compromise choice. Cases like this would have to technically be called a "tie" in Condorcet and something would have to be done to break that tie. In politics of a left/right spectrum, it is very hard to imagine such cycles, but possible given different people voting on different issues.

Hybrid systems can also be constructed that combine a plurality count elimination round AND a Condorcet pairwise round. The plurality count eliminate weaker candidates in a first round, a head-to-head count among the remaining strong candidates determines the winner.

The plurality elimination round could have different thresholds of survivability:

A simple elimination rule might be: Eliminate all candidates who have at least half as many votes as the plurality candidate OR keep at least the top-two candidates.

Of course the SIMPLEST hybrid system is the "top-two instant runoff" system. Condorcet is trivially reduced to a single pair of candidates in the second round. If you want more than 2 candidates to survive the first round, then Condorcet offers a way to treat these candidates fairly without elimination.

CONCLUSION

That's my simple summary of voting systems that support the principle of majority rule. There's many other systems you can consider - Borda, Approval, Bucklin, Ratings, but most of the other systems fail to support the "one person, one vote" ideal of democracy. That doesn't mean they are worthless, but it means we'd need to change a most fundamental principle of democracy.

So when you hear ideas like "Instant Runoff Voting" supports Majority rule, know this is true, but there's other equally good approaches to consider. Myself, I'll support any of the 5 methods above (or variations), and if IRV is the most viable path, I'll take it.

Comments are welcome.