The scheme of voting most familiar to people in many countries is simple plurality voting. Several candidates are offered, and one chooses a single candidate to put one's X beside, and the candidate that gets the most votes wins.
If there are only two candidates, this method accurately selects the candidate most people prefer, and, in practice, this is effectively often the case, at least approximately.
It may well be a good thing that a political party in third place has to first exchange places with the party in second place before having a chance of winning. A tiny party expressing ideas that are popular might be lying about its real intentions, according to which it will act once it gains power. There are other ways of dealing with that danger, such as bicamerality, or a constitutional monarch who can dissolve Parliament at will. One could allow the Supreme Court to call an election when, in its opinion, the government has violated its campaign promises: making an election campaign promise a binding contract between an elected ruler and his people would be an interesting - and novel - idea.
However, favoring the largest parties also favors the largest advertising budgets. And limiting what a party can spend on an election campaign can end up limiting freedom of speech, as we have seen.
Two major schemes have been suggested for allowing elections to produce results more closely in accord with the popular will.
One is called the Single Transferable Vote, or Preferential Voting. In this system, instead of an X, one marks a 1 next to the candidate one first prefers, a 2 next to one's second choice, and so on.
When the ballots are counted, in the first round, one counts only the "1"s marked on the ballots. If no candidate obtains a simple majority of the votes cast, then the candidate who won the least 1 votes is eliminated, and the ballots for that candidate are then distributed among the other candidates according to the "2"s marked on them in the second round.
The remaining candidate with the least votes is eliminated to begin the third round, and his votes are distributed among the other candidates based on the next preference on them, whether a 2 or a 3. And this continues until only two candidates are left, when there must be a winner.
The strength of this technique is that if the majority of people in a riding, constituency, or district favor a candidate of one type, but are closely split between two candidates in that group, while the opposing kind of candidate is supported by a large minority, the candidate opposed to the majority choice in the riding cannot win simply because of a split vote. Thus, voters in the majority group are free to use their vote to choose the candidate that more exactly represents their particular flavor of the majority sentiment.
The weakness of this technique is that if the majority of voters in the riding are almost evenly split between two strongly opposed groups, then a compromise candidate who is the first choice of only a few would be eliminated at an early stage, and would not be available as an alternative in the last round, even though the compromise candidate might be preferred to the winner by a majority of the voters.
I propose below a method to eliminate the weakness and retain the strength.
Another is called Proportional Representation. Here, the number of candidates in a legislative body belonging to a single party is determined by the percentage of votes going to that party.
The most straightforwards way of implementing this system is known as the party-list system. If there are 100 seats in the legislative body, each party in the election presents a list of 100 candidates, in order of preference; if the party wins 5 seats, the top 5 candidates on that list are elected.
The aim, and the strength, of this form of voting is that the legislature more closely approximates, in the area of party standings, a mathematical model of the country as a whole.
However, this makes centralized parties very powerful, and means that if a country is divided into different regions with different views and interests, this is only expressed in the legislature if the different areas are represented by different parties.
A Canadian author proposed dealing with this flaw by having an election with individual ridings, but still filling the legislative body according to proportional representation; this would be done by choosing candidates other than the local winner in some ridings, where the support for the local winner's party was weakest, and that for the party whose support was diluted was strongest. He felt confident that when this happened, people in an affected riding would still regard the elected candidate as their representative, even though most of those in the riding voted for someone else. I do not share this optimism, but I propose another scheme which may deal with this.
For various reasons, proportional representation tends to be supported by some people on the Left, while preferential voting tends to be supported by some people on the Right. Thus, I suspect that what should be done for the best balance is to have a bicameral legislature, with both houses elected, the lower house being elected by proportional representation, and the upper house by preferential voting.
Another problem with proportional representation is how one would limit the number of parties presenting themselves on the ballot. Having a bicameral system would allow a simple rule to be used; for a party to present itself in the proportional vote for the lower house, it would have to have either one elected member, or a second-place runner up in any of the rounds of ballot counting for any riding, in the upper house. This would have the additional effect of having the same parties contesting both houses.
It has been proposed before to improve preferential voting. Many schemes have been tried, such as small multi-member constituencies. Others have only been proposed, such as looking for both a "Condorcet winner" and a "Borda winner" of an election, and choosing one if possible, or the other if the one does not exist.
I propose a simple scheme of modified preferential voting which allows a compromise candidate to win where appropriate but which follows a simply-explained mechanical procedure.
In the first round, the number 1 votes are counted. The candidate with the least number 1 votes, instead of being completely eliminated, is categorized as "inactive".
In the second round, the ballots cast for the newly inactive candidate are then distributed among the other candidates based on their number 2 votes. However, the number of votes the inactive candidate had are still noted, and the number remains associated with that candidate.
To prepare for the third round, the active candidate with the least number of votes is moved to the inactive group. The total votes that candidate had remain noted for that candidate. Now, those ballots are then distributed based on their next vote. But if that next vote is for the other inactive candidate, although the ballot ultimately ends up with the active candidate who gets the vote after that, a vote is still added to the total for that inactive candidate as well.
If there is a tie for lowest place in any round, both candidates are moved to the inactive group. Successive rounds proceed as the third round.
The final round is the one in which there is only one active candidate. In that round, that candidate wins, unless one of the inactive candidates has a larger total of votes that passed through that candidate than were received finally by the last active candidate, including received from the second candidate last eliminated.
How can we have an election in which the results are proportional to party preferences, which also involves constituencies, and yet allows people to always have representatives of their own who represents their views?
Here is a scheme that I think is original.
Let us divide up the country into 128 ridings, and, by means of those ridings, elect members to a legislative body with 255 seats.
People cast an X for the candidate of their choice, but this selection also indicates a party preference.
For each of the 128 ridings, the candidate with a plurality of the votes in that riding is elected in that riding.
The ridings are, prior to the election, grouped in pairs of geographically-adjacent ridings.
Each pair of adjacent ridings has three elected representatives, the two which represent the two individual ridings of which it is made, and a third who represents the pair of ridings at large. The third is chosen so that the three seats for the two ridings are distributed according to proportional representation, as closely as possible. Of course, it could happen one has two ridings with 102 votes for party A, 99 votes for party B, and 98 votes for party C. In that case, the proportional result would be one candidate each for parties A, B, and C, but since two candidates for party A are already elected, the best that can be done is to select the third representative from party B, if ridings stay fixed. Or, the ideal proportional result can be retained, but then all three representatives for the pair of ridings represent only the pair of ridings at large. Presumably, this phenomenon, which could be called "melting", would only take place if necessary to maintain the final result.
Then, another candidate represents a pair of adjacent pairs of ridings, and is chosen according to the same scheme. The ideal proportional result is that determined by the Hamiltonian scheme rounding; when a fixed number of seats must be filled, one goes through the odd fractions of a seat in order, starting from the largest, to award the seats left over when every whole seat earned has been distributed.
With nearly half the representatives not coming from individual ridings, it should seldom be necessary for "melting" to descend to the level of the individual riding. The phenomenon of "melting" ensures that no candidate not part of a fair representation of a small area is labelled as the representative of that small area alone, and allows perfect proportional representation without an override. Note also that this proposal is not fully defined, unlike that for an improvement to preferential voting.