This is a quick note to describe a voting system that I’ve toyed around with a while, and which I have implemented as an option for decision-making among participants in an aftok.
When I describe a “fair” system, I have a few specific properties in mind. These may bear little relationship to fairness as described by Condorcet or Arrow’s Theorem, but they’re the properties that I think are important. Many of these properties are corrective in nature; they are derived from the flaws of the systems that are in current use, or have been proposed.
Criteria
The system must admit any number of candidates/options without creating a “spoiler” effect (violated by plurality systems.)
The system must not compel any voter to provide a ranking for a particular candidate (supported by range/approval voting, violated by Borda count, some variants of RCV.)
It must be possible for a voter to vote in a way that accurately reflects their opinion of each candidate (supported by range, violated by approval and random ballot.)
Every vote must be significant - that is to say, it must be possible (though potentially improbable) for the opinion of any voter, even a voter in a tiny minorty, to be reflected in the final result. (violated by everything except random ballot.)
To achieve this set of criteria, I propose the following system. It derives significantly from both range voting and the random ballot. The system depends upon a deterministic, cryptographically secure pseudorandom number generator and a secure hash algorithm. The system proceeds in three phases:
Voting Procedure
Prior to the election, a randomly generated salt value must be published to the electorate.
For the vote itself, each voter completes a ballot as for range voting, having the option to select a rating between 0 and 10 for each candidate. In addition, each ballot provides a “disapprove” option for rating, which permits the user to state to what degree they disapprove of all available candidates. “Disapprove” is, for the remainder of the process, treated as any other candidate. If, upon completion of the process, the “disapprove” candidate is selected, a new election must be held, with all current candidates from the failed election barred from running.
Prior to counting, the ratings selected by each voter for each candidate are normalized based by dividing by the sum of that voter’s ratings. This ensures that each voter’s aggregate contribution to the overall result is the same.
Ballots are counted as with range voting - the voters’ ratings for each candidate are summed to produce an integer-valued tally for each candidate. The resulting totals are published. Along with these results, a timestamp specifying some time in the near future (for example, a day from the time of publishing) will also be published.
At the moment of the specified timestamp, a second salt value is derived from some publicly visible, time-dependent but non-manipulable value (for example, the hash of the most current block in the Bitcoin blockchain) will be recorded.
Starting with the candidate with the highest vote count, and proceeding to the candidate to the lowest vote count, the hexidecimal string values of each candidates’ vote counts are concatenated. To the end of this string, two additional values are concatenated: the salt value published prior to the election, and the salt taken subsequent to the election.
The resulting string is used as the seed for the deterministic, secure random number generator with uniform distribution. This generator is then used to select a random value from the unit interval.
The published vote counts are then used to allocate break points in the unit interval, from highest count to lowest count. Essentially, each candidate, from highest to lowest, is allocated a percentage of the unit interval corresponding to their rating sum. The winning candidate is the candidate within whose portion of the unit interval the randomly selected value falls.
Justification
The system described here has several features not present in other voting systems. From its weighted pseudorandom selection, it derives a degree of fairness not present in other systems - every candidate has the potential to win, but a highly approved-of candidate will be selected with high probability. The system is also, by virtue of this randomness, virtually immune to manipulation by dishonest actors in the vote-counting process - any effort to influence or subvert the vote-counting process is likely to be wasted.
Secondly, the value of tactical voting is minimized. If a voter approves of several candidates, but disapproves of others, no significant advantage would be gained by limiting their allocation of votes to any candidate whom they approve of.
Due to the presence of a “disapprove” option, it is possible that no candidate from a given round may win. This promotes a desirable features: candidates must attempt to have broad appeal to have a reasonable shot at winning, but this need to seek broad appeal is in tension with the possibility that the election may need to be re-run. In our modern world of outsize campaign spending, political parties take a risk by committing significant funds to the support of a single candidate. In addition, this feature would hopefully limit the influence of individual personalities in the election process - however, whether this effect would materialize in practice is something that should be empirically determined.
Objections
One obvious objection that there is no guarantee that the most highly-approved candidate be selected. This is in fact considered a feature by the author of this system - in a closely contested race, there is little reason to believe the public good is best served by a candidate who wins by a narrow margin. From a utilitarian perspective, if an electorate is split nearly 50/50, there is little reason to believe that one of the candidates will better serve the good of the entire electorate better than the other.
A second objection is that, even though the probability is low, it is possible that a despicable candidate might be selected. This complaint rests upon the assumption that the supporters of such a widely despised candidate are not worthy of fair representation. If we as a society are genuinely commited to the equality of all people, then the opinions of all, however despicable, must have at least some minimal chance of being represented.