Why the "quorum rule" – rule "d"?

The purpose of rule "d" is to prevent candidates whom almost nobody has ever heard of, from being elected by a few radical supporters. For example, if 99.9% of the voters never heard of Andreas Q. Snickelgruber and all gave him an "X" (intentional blank) and the remaining 0.1% of the voters were part of his secret world-takeover cabal and all gave him 99 (maximum possible score) then Snickelgruber would win! Horrors!

Except: rule "d" prevents that – saving the world – Snickelgruber cannot win unless he gets at least half the score-sum garnered by the candidate with the greatest score-sum. (And note, at least one candidate surpasses this hurdle!)

Note: I personally regard the world-takeover plan as ridiculously unlikely even without rule d. (Also, if you want to worry about the "stealth candidate" bogeyman, then worry about Democratic & Republican stealth candidates under the current plurality system!) Anyhow: be not afraid – rule d is there to save you from that tiny risk.

On the positive side – the rule d safeguard may have the good benefit of causing voters who wanted to write X, but without rule d would have been too afraid to do so and would have voted 0 to "play it safe" – now to do so. That less-fear-based behavior will have the benefit of yielding a more-honest evaluation for Snickelgrubers. That is good because more voter honesty is good: If Snickelgruber gets a high score but is not elected (either due to rule d or because somebody else got a higher score), Snickelgruber's days of anonymity will be over and now he can aspire to office in a future election. That is good because it naturally tends to bring good candidates into the public eye.

Also note: if all voters score all candidates, i.e. nobody uses intentional blanks, then the quorum rule has no effect.

Write-in candidates

One can argue the quorum rule is necessary to make range voting behave sensibly if we permit write-in candidates who can run for office but whose name is not listed on the ballot.

It is rare for write-in candidates to win an election. It is less rare than I once thought – e.g. the longest-serving US senator, segregationist and all-around hypocrite Strom Thurmond, was originally elected as a write-in; and California congressman Ron Packard was also. (Henry Cabot Lodge Jr. won the 1964 Republican presidential primary as a write-in without even officially running, thanks to a small group of Republican activists. Lodge's 35.5% beat B.Goldwater's 22.3%, N.Rockefeller's 21%, and Richard Nixon's 16.8%.) But still, it is quite rare: as far as I currently know, there were only a handful of write-in US congress & senate winners out of over 10,000 races conducted. It is actually probably more common for a write-in candidate to get exactly one vote (presumably their own) than it is for one to win.

Without the quorum rule (and with voters who do not mention a write-in candidate on their ballots being regarded as awarding him "intentional blank" scores), range voting could behave very badly by always electing such unknown one-vote write-ins! With the quorum rule, victory by a write-in candidate becomes (just like now) very difficult (although possible – in exceptional circumstances such as this, where it presumably would also have happened under range voting). But, fairly, there is no particular bias against write-ins – if they have quorum-level voter response, then they can get elected.

Comparison of range voting with other voting system proposals re how they handle write-in candidates

Voting systems How it handles write-ins
Range (averaging, blanks allowed, no quorum rule) Bad behavior. Always elects unknown write-in candidate (if one exists).
Range (score-summing, blanks treated as zero score, no quorum rule) Unknown write-in candidates almost impossible to elect. But still bad behavior: bias against lesser-known (rather than lesser quality) candidates.
Range (averaging, blanks allowed, quorum rule) Unknown write-in candidates almost impossible to elect. No bias against lesser-known (rather than lesser quality) candidates, provided they are well-enough known to reach quorum. Good behavior.
Condorcet systems (truncation allowed, unmentioned candidates treated as ranked coequal bottommost) Bad behavior: extreme bias against lesser-known candidates. Extremely difficult for a write-in to win.
Condorcet systems (truncation allowed, unmentioned candidates treated as uncompared to mentioned ones) Bad behavior. Always elects unknown write-in candidate (if one exists).
Condorcet systems (ballot truncation forbidden) No such thing as a write-in candidate.
Condorcet systems (voters allowed to express or not express info about each candidate-pair independently) This allows voters to express the information they know but avoid saying what they don't know, similarly to range's "blank score" option. But it leads to bad behavior. Voters need to express tremendous amount of information in a race with large number N of candidates: (N-1)N/2 bits of info. Also very difficult to tell if vote is valid, i.e. does not contain a logical inconsistency. Also, it could lead again to surefire election of an unknown write-in candidate (if one exists).
IRV (ballot truncation forbidden) No such thing as a write-in candidate.
IRV (ballot truncation allowed) Extremely biased against write-in candidates.
I thank David Stephenson for educating me about write-in winners.

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