Range Voting versus other voting systems

SUMMARY CHART of voting system properties

Please view widescreen.

Voting system Expressive Participation (avoids "no show paradoxes") Favorite-
Monotonic Remove-
Enactability Simplicity
Plurality The Worst yes FAILS! FAILS! yes FAILS! yes yes Extremist (already enacted) good
Approval or
on each canddt
yes yes partial yes yes yes yes voter-
or unbiased)
good best (excellent for meetings)
Condorcet systems rank order FAILS! (2.5%?) FAILS! yes & no
(some obey it)
yes & no
(some obey it)
FAILS! 9% yes & no
(some obey it)
FAILS! unbiased probably bad complex
Borda rank order yes FAILS! FAILS! yes FAILS! yes FAILS! ok ? medium
Instant Runoff (IRV) rank order FAILS! 16.2% FAILS!
yes FAILS!
FAILS! (13%?) FAILS! FAILS! Extremist bad complex
Range The Best yes (if no "blanks") yes yes yes yes yes surprisingly yes ok (bias, if any, small) best surprisingly good

Definitions of the common Single-Winner Voting Systems in one crib sheet

System What is a "Vote"? Who wins?
Plurality Name one candidate then shut up ("Nader") The most-named candidate.
Runoff "Name one candidate" again – except there might be two elections Top-two from 1st round get to be in 2nd (but only 1 election needed if "majority winner")
Borda Rank ordering of all candidates ("Nader2>Bush1>Gore0") "Borda Score"=Get K points for each voter who ranks you K slots above bottom. Highest summed score wins.
Condorcet Rank ordering of all candidates ("Nader>Bush>Gore") If someone exists who beats every rival pairwise, then wins (else tricky; numerous rule-flavors)
"Instant Runoff" (IRV) Rank ordering of all candidates ("Nader>Bush>Gore") Eliminate "loser" candidate top-ranked by fewest voters (eliminated both from election, and from all ballots). Now repeat that over & over until only one remains (who wins).
Approval = Range1 The set of candidates you 'approve' e.g. {Bush, Nader} The most-approved candidate.
Range9 Award score in 0-9 range to each and every candidate, e.g. "Bush=5, Gore=9, Nader=9" Candidate with highest average score.
Range99 Award score in 0-99 range to each and every candidate, e.g. "Bush=50, Gore=99, Nader=99" Greatest average score wins.

There are many other voting systems too... Also there are many Variant Rules for these systems...

Australia forces IRV voters to rank-order every candidate. Other places allow voters only to order some & omit others (automatically last-ranked). Some places force voters to rank their top K choices (for some fixed value K, such as 2 or 3) but no more. In range-voting, "no opinion" ("X") scores can also be permitted; these do not affect a candidate's average (then is common to refuse to permit somebody to win if he has too-few genuine, i.e. numerical, scores).

Example Election

#voters Their Vote
4 A>D>E>C>B>F
3 B>E>D>F>C>A
2 C>B>E>D>F>A
1 D>C>F>A>E>B
1 F>C>E>D>B>A
An 11-voter, 6-candidate election (candidates A,B,C,D,E,F)

Plurality: A wins (most top-rank votes with 4).
Plurality+Runoff among top two: B wins over A in the runoff, 6-to-5.
Instant Runoff (IRV): C wins (eliminate E, D, F, and B in that order – doesn't matter which way you break DF tie – then C beats A in final round 7 to 4). IRV repeatedly deletes the candidate with fewest top-rank votes, then the remaining one wins.
Borda: D wins. (D's Borda score is 16+9+4+5+2=36 versus E with 12+12+6+1+3=34 and with lower scores for A, B, C, and F.) In the Borda system a candidate gets awarded 0 points if ranked last, 1 if ranked second-last, 2 if... and the candidate with the greatest score-sum ("Borda count") wins.
Condorcet: E wins. (Since E pairwise-beats each other candidate, e.g. beating A 6:5, B 6:5, C 7:4, D 6:5, and F 9:2.)
Approval Voting: If all the red candidates are "approved," then F wins with 7 approvals (versus A=4, B=5, C=3, D=6, E=5).

And with 0-99 Range Voting, it would in fact be possible to make any of the 6 candidates win, depending on how the voters chose the scores compatibly with the orderings above. In Range Voting each voter awards a score from 0 to 99 to each candidate; greatest average score wins. (Fancier rules allow also scoring a candidate with X = intentional blank = "no opinion" – only numerical scores incorporated into averages.)

Properties voting systems may or may not have

Expressiveness: The more kinds of votes you can cast, the more expressivity you have. With plurality voting in an N-candidate election, you have N possible votes (or N+1 if "not voting" is allowed and we count it as an additional option). That is a lot less expressivity than approval voting with 2N possible votes. With rank-order voting systems you have N! (although in such rules-variants as top-3-IRV there are much fewer legal votes; e.g. approval voting is more expressive than top-3-IRV if there are more than 8 or 9 candidates, such as in San Francisco's top-3-IRV mayoral election of 2002 with 12 candidates plus 6 more running as write-ins) and with 0-99 range voting you have 100N (or 101N if "no opinion" scores permitted for each candidate).

Participation: If casting an honest vote can never cause the election result to get worse (in that voter's view) than if she hadn't voted at all, then that voting system satisfies the "participation property." (Some voting systems like Condorcet and IRV fail this – they exhibit "no-show paradox" elections where some class of voters would have been better off "not showing up.")

Favorite-safe: If it never is more strategic to vote a non-favorite ahead of your favorite, then the voting system is "favorite-safe." (So-called because it is "safe" to vote for your favorite.)

Clone-safe: If a "clone" of a candidate (rated almost identical to the original by every voter) enters or leaves the race, that should not affect the winner (aside from possible replacement by a clone). We call voting systems obeying this "clone-safe." Borda and plurality voting severely fail this property.

Monotonicity is the property of a voting system that

  1. If somebody increases their vote for candidate C (leaving the rest of their vote unchanged) that should not worsen C's chances of winning the election.
  2. If somebody decreases their vote for candidate B (leaving the rest of their vote unchanged) that should not improve B's chances of winning the election.

Remove-loser safe: If some losing candidate X is found to be a criminal and ineligible to run, then the same ballots should still be usable to conduct an election with X removed, and should still elect the same winner. (But if X's departure changes the winner, the property fails. In several voting systems, e.g. Borda, X's departure can actually reverse the finish-order of all the other candidates, a dramatic failure.)

Precinct-countable: If each precinct can publish a succinct summary of the vote (sub)total in that precinct, and the overall country-wide winner can be determined from those precinct subtotals, then the voting system is "precinct-countable." Precinct-countable systems allow greater election transparency to reduce risk of undetected fraud.

Dumb machines: Are "dumb" (i.e. non-computerized) totalizing voting machines, designed only to support plurality voting, usable for this voting system?

Extremist/Centrist bias: Suppose the candidates are positioned along a line (1-dimensional) or in a plane (2-dimensional) and voters prefer candidates located nearer to them. In some voting systems, it is usually difficult or impossible for "centrists" (centrally located relative to the other candidates) to win. Those systems "favor extremists." Other voting systems "favor centrists." We apologize for defining this property rather vaguely, but in practice it is often quite clear which category a voting system belongs in. For example, check these pictures (especially "note #2") to see that Instant Runoff (IRV) voting strongly favors extremists; more such pictures for many other voting systems here showing that, e.g, plurality voting also has built in pro-extremist bias.

Relative Enactability: This is judged from poll studies about voter preferences. (Click the link for details.) These show range voting is the most enactible (with 10 score-levels apparently most preferred), approval voting next, plurality next, and instant runoff is the least enactible (and most likely to be repealed) among these four.

Also, historically: approval, score, plurality and instant runoff all have been enacted in various countries. (Borda was enacted just once, but soon repealed.) As far as we know Condorcet was never enacted and also never was put to a referendum to try to be enacted. But considering it is even more complicated than IRV its chances seem probably poor.

Simplicity: Voting systems with simpler rules, simpler counting algorithms, and found to be simpler by human voters are "simpler." If you want to be precise about this, then we point out you can objectively measure the "simplicity" of the rules and vote-counting algorithm as the length of the shortest computer program that inputs, checks-validity-of, and counts the votes to determine the winner. And you can objectively measure how simple humans find it to vote by e.g, comparing ballot spoilage rates under different voting systems, or comparing the average time it takes humans to cast their vote or for other humans (or computers) to count them, or asking voters for their self-assessed comprehension level. The latter two actually indicate, surprisingly, that range=score voting is the best-comprehended among {score, approval, instant runoff} *– and perhaps even if we include plurality too! – i.e. the situation is better for range voting than our chart indicates.

Another voting system chart, by Robin Quirke

Another voting system chart, by Ka-Ping Yee (pdf, does not include score voting among methods compared)

Return to main page