Generally speaking, we regard range voting as the best single-winner voting system, for a wide variety of reasons.
However, approval voting, which is the maximally-simple degenerate special case of range voting, can for some purposes be superior.
Approval voting is probably the simplest voting system in the world. It is even simpler than plurality voting because there is no rule about "overvotes" being illegal (and therefore no need to detect overvoters to punish them). To switch from plurality voting all you need is to change the instruction "vote for one" to "vote for one or more." Simple. Total cost of switching: zero.
Range voting seems superior to approval voting because it allows more expressivity (some candidates can be approved, some "highly approved", some "very very disapproved" etc), but unfortunately it is more complicated. Although both approval and range voting can be run on all voting machines, with the worst kinds of voting machines approval could be significantly easier for voters than range voting.
Also, for use in votes at meetings you can do approval voting by simply raising your hands (or better, holding a red card in your raised hand) and counting the hands that approve of X. Trying to do range voting, Borda voting, Condorcet voting, and etc would be far slower and more error-prone. Further, plurality voting also is error-prone because there is no easy way to be sure that some of the 1000 people in that room have not (illegally) voted twice. That makes it easy to cheat in plurality votes in large meetings – besides the fact plurality is a worse voting system than approval anyhow.
We do not actually regard range and approval voting as competing because approval voting is just a special case of range voting and the two can peacefully coexist.
So if every voter tries greedily to maximize his own personal wealth and happiness when choosing his vote, the result will be the election of the best possible candidate maximizing total money-benefit to all. This voting system is thus "perfect"!
Before you get too excited about the "perfection" of this scheme, though, we point out a few problems.
In view of all this, it seems to us that CTT voting might work well in corporate stockholder votes in corporations that have between 1000 and 100,000 stockholders, with the voter payments ("Clarke taxes") donated to charity. For that purpose the US constitution does not forbid CTT, and the CTT voting system's perfection will actually pretty much happen (if the system is designed carefully) because the mathematical assumptions will in fact then be approximately true in the real world – and, if so, CTT voting will yield the best corporate profits. But for corporate votes with too few or too many stockholders, range voting with one range vote cast by each share of stock, is probably better.
More generally, corporations that adopt superior voting methods such as range voting to make hiring decisions at meetings, etc, will, slowly but surely, enjoy steadily compounding advantages over their rivals that use poor voting methods such as plurality or Borda because they will, on average, make better decisions – and this improvement comes at a cost of zero. To corporations we say: there is probably no move you can make that will give you this large an improved competitive advantage over your rivals, that is, at the same time, this easy and cheap to implement. (Talk about a no-brainer!)
We discuss CTT voting in far greater detail here, including making some significant new realizations and improvements that seem essential for good performance in practice.
We do not know what is the best voting scheme based on ballots which are rank-orderings of the candidates. Quite possibly, no clearly-best such scheme exists. Every scheme we are aware of does something horrible in at least one election-circumstance. And that is not just due to our ignorance – there are impossibility theorems saying that every ranked-ballot scheme (whether anybody has invented it, or not) fails to satisfy at least one of a list of desirable-sounding criteria, in some elections. There just is no ranked-ballot scheme that clearly is head and shoulders above its rivals. We are therefore very hesitant to suggest one.
There are many problems with the whole idea of rank-order ballots, but they all fundamentally spring from these two difficulties:
Incidentally, one could optionally permit or forbid equalities in the rank-ordering (e.g. "A>B=C>D=E>F") and one also could permit or forbid only ranking some but not all of the candidates (e.g. "A>D>F"), and these may alter the view of what the best voting system is.
However, if you really, really, really push us hard to choose a system, and you insist (in our view very foolishly) on using rank-order ballots, then Schulze beatpaths and WBS-Irv seem tolerably decent attempts to save you from yourself.
(For example, electing a "committee" of 5 people from 23 candidates.)
The trouble with naively applying some scheme designed for single-winner elections (such as range or plurality voting) to the committee-problem, is the quality of a committee is not about just the sum of the perceived qualities of its members. It is also about diversity.
For example, if an electorate contains 51% Whigs and 49% Tories, then using either range, plurality, approval, or instant-runoff voting with the top 5 scorers being elected, we might well elect a 100%-Whig committee! We don't recommend that. It would probably be better to elect 3 Whigs and 2 Tories.
That is the goal of proportional representation systems.
It is much harder to compare multiwinner systems than it is to compare single-winner systems, because for the latter problem we have the powerful Bayesian Regret yardstick available. Also, multiwinner systems have been less investigated.
Nevertheless, we do have two such systems to recommend:
These two systems are described in papers 77 & 78, and multiwinner systems generally are surveyed in paper 91, here.
Asset voting is simple enough that we can describe it here in full:
Asset voting to elect W winners from C candidates, 0 < W < C:
In variants, only certain kinds of redistributions are permitted, for example the candidates in increasing order of "wealth" drop out, redistributing their assets among the remaining ones as they do so. This "poorest first" variant has the advantage that it forces the procedure to end quickly and everybody knows when it has ended. Forest Simmons recommends that electorates that don't want to deal with any ballots other than Plurality style ballots, should use a simpler version of Asset Voting or that uses only Plurality-style ("name one candidate") ballots (the named candidate gets 100% of that voter's assets).
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