Voting Rules for
 Accurate
Democracy

Different uses for voting need different types of voting.

A voting cycle is a tie for a Condorcet rule

Loring One-winner Rule

Parliamentary motions with Condorcet rules

Instant Runoff Voting Resists Manipulation

In the 1970s, mathematicians proved every voting system can be manipulated, sometimes.  The question then was, can some be manipulated more easily or more often than others?  Researchers found:
“The most striking result is the difference between the manipulability of the Hare [IRV] system and the other systems.  Because the [IRV] system considers only 'current' first preferences, it appears to be extremely difficult to manipulate.  To be successful, a coalition must usually throw enough support to losing candidates to eliminate the sincere winner (the winner when no preferences are misrepresented) at an early stage, but still leave an agreed upon candidate with sufficient first-place strength to win.  This turns out to be quite difficult to do.”  Chamberlin, Cohen and Coombs (Ref. C)
Often impossible.

As they imply, first preference is the rank most likely to be sincere on a ballot.  It is hard to convince voters they will get a better result by lying about their first preferences.  Merrill reports that findings by Tideman agree with these and states, “Indeed, since the Hare [IRV] system appears very difficult to manipulate, strategic voting tends to be identical with sincere voting...” (Ref. M)

But the same researchers also found IRV poor at electing the most central option; it is often encircled by rivals, gets few first-rank votes, and is eliminated in an early round of ballot counting.  [Hare's rule is often called Instant Runoff Voting (IRV) in the USA, Alternative Vote (AV) in Australia, and Preference Vote or Single Transferable Vote (STV1) in Europe.]

Enacting the majority policy, the Condorcet winner, is a key criterion for measuring democracy.  IRV fails in simulated elections less often than plurality rule but more often than Borda and some others.  However, Borda and other rules often reward manipulation by strategic voting and so encourage it.  So in competitive elections they do not even start with the sincere ballots needed to find a majority policy.  Finding the best policy is the primary reason to block manipulations.  Increasing trust is a deeper benefit.  

Condorcet + IRV, the Best of Both ?

Several people have invented voting rules that resolve voting cycles by combining Condorcet's rule with Hare's rule in various ways.  Each of these hybrid rules enacts the Condorcet winner when there is one.  When a cycle occurs, it uses the Hare process of eliminations and transfers until one option tops each of the other remaining options.

David Hill, formerly of England's Electoral Reform Society, proposed in 1988 making the current Condorcet winner exempt from elimination at each step in an IRV tally. His goal was to make one excellent rule for both single- and multi- winner elections. (Ref. H)

Robert Loring, formerly of FairVote, proposed in 1990 changing the criterion for winning Hare from a majority of ballots to the Condorcet criterion.  This eliminates the option which holds the top rank on the fewest ballots - until one option can top each of the others 1-against-1.  To focus on the tally process, we might call Hare's rule "Majority-IRV" (M-IRV) and Loring's variation rule "Condorcet-IRV" (C-IRV).

Note: The 1990 paper used data from Chamberlin and Merrill, so it was mailed to them, asking for and receiving permissions to use the data you see on the comparative data pages.  It was published on the Web in 1997; the InternetArchive WayBackMachine has a very different version stored on August 16, 2000.

Nicolaus Tideman, of Virginia Tech, proposed a rule that eliminates any options outside the smallest voting cycle (Smith set), and then eliminates the option with the fewest first-choice votes.  This repeats until only one candidate remains.

Loring One-winner Rule (LOR) for legislative voting builds on these rules.  It elects the Condorcet winner if there is one.  If there is none, LOR finds the C-IRV winner and the chairperson's favorite; then tallies a runoff between these two.

All 4 tallies: Condorcet's rule, IRV, the chair's tie-breaker or another completion rule, and the final runoff, all are tallied from the preference ballots.  Each rep casts 1 ballot and the series of tallies is automatic.
 

The only way to manipulate Condorcet's rule is to create a sort of tie -- a “voting cycle” in which no option can win majorities over every single rival.  IRV is manipulable rarely.  Tactical votes cannot manipulate a chair's ballot or a 1-on-1 runoff.

If the majority option is in the final runoff, it will win.  For LOR to fail, Condorcet, IRV, and the chair all must fail to find the central option.  Of course, they could fail simultaneously.  But the chance of that is less than the chance of failure for the best element of LOR.
 

The need to create a voting cycle may make LOR even harder to manipulate than IRV.  Creating a cycle sometimes requires more conspirators than a manipulation of IRV does.  Thus LOR often increases the number of reps who must be organized into a conspiracy.

In order to manipulate LOR, a group must 1) create a voting cycle and either 2a) manipulate IRV, or 2b) chance upon a case in which IRV does not enact the Condorcet winner.  Thus LOR could be easier to manipulate than IRV only in 2b, when IRV fails to enact the policy preferred by a majority.

3) In addition, LOR calls for a final 1 against 1 test if IRV and the chairperson disagree.  This runoff step increases the risks for strategic voters.  When the true Condorcet winner is 1 of the 2 finalists, a crossover strategy will give the manipulators a result no better than the Condorcet winner.  (In B versus C, C wins.  In D versus C, D wins and the conspirators get a result they like less than the Condorcet winner, C.)
 

When there is no Condorcet winner, LOR picks from the Smith Set (the candidates in the voting cycle) both the IRV winner, because that is the hardest rule to manipulate; and the option ranked highest by the chairperson, because she has the least incentive to create a cycle.  (The chair's ballot or the IRV tally or both may be replaced by hard-to-manipulate rules such as Tideman's Ranked Pairs or the Schulze method.)

Procedural Rules

Those completion rules are very good -- so further reducing opportunities for manipulation, its ease and safety, are very tough goals.  Another way to improve legislative voting is by procedural rules.  Here is a common one, adapted to ranked-choice ballots.

Strategic voting often gives the strategists a risk of enacting a policy that they would like less than the winner from their sincere voting.  That is the aim of this procedural rule, to increase that risk and so deter attempts:

Anyone who ranked the runoff winner over the loser may move to change that vote.  Other reps may change their votes also at that time.  This motion to “Recall the Question” returns only to the runoff stage.

(Voters might ask for endless minor revisions if they were allowed to return to the full rank ballot.  That also could increase information available for manipulation and counter-manipulation.)

Reps might change their runoff votes if they see in the ballots a likely manipulation such as voters “crossing over” the center to support an opposing policy (which had no chance of winning).  That can create a voting cycle if the opposing policy beats the most central policy.  Such ballots may be obvious.  If so, re-voting gives the majority a chance to punish the schemers by enacting the crossover item.

Footnotes:

James Green-Armytage explains Four Condorcet-Hare Hybrids.
He also lists eight Anti-strategy enhancements for Condorcet methods.

Monotonicity
Monotonicity criterion: If X is a winner under a voting rule, and one or more voters change their preferences in a way favorable to X (without changing the order in which they prefer any other alternatives), then X should still be a winner. Conversely, if they lower their ranks for a loser, that candidate should still lose.
IRV is sometimes non-monotonic. If that happens, there are several ways it might effect an election.
I) Strategic voting: How often can a like-minded group of voters improve their result by raising a low choice above a higher choice?
II) Sincere regrets: How often does a sincere ballot hurt a like-minded group of voters? There are two parts to this:
A) How often would a group have seen a better result if they had not voted?
B) How often would a group have seen a better result by raising a low choice above a higher choice?
III) What does it matter:
A) How often could a group have hurt a candidate, whom they liked, if they had raised her rank?
B) How often could a group have helped a candidate, whom they disliked, if they had lowered her rank?

No one has published research showing how often Condorcet-Hare hybrids are non-monotonic. In a small percentage of elections a voting cycle prevents a Condorcet win. In what (small) percentage of these cycles does IRV give sincere regrets? And in what (tiny) percentage of the cycles does IRV give a safe chance for strategic voting?

About research on manipulation:

Using preference ballots from a large association's presidential elections, with 5 candidates in each, University of Michigan Professors Chamberlin, Cohen, and Coombs researched how often 9 voting systems were manipulable and how easy the manipulations were.  The rules were plurality, Borda, Hare (IRV), Coombs, approve 2, approve 3, and the Condorcet completion rules Kemeny, Min-max, and Black's (Condorcet then Borda).  The other rules were manipulable in all 10 tests, but IRV was manipulable in only 1.  Truncated ballots with some options unranked were not allowed.

Virginia Polytechnic Institute Professor Nicolaus Tideman found similar patterns and conclusions using preference ballots from 87 medium-sized, multi-winner elections. “the alternative vote is quite resistant to strategy” and “the fact that in 87 elections in the sample there were just three in which there was a dominant option [Condorcet winner] that was not chosen is somewhat reassuring.”
(Collective Decisions and Voting: The Potential for Public Choice, Ashgate Publishing, 2006, pgs. 194-195).

In The Burr Dilemma in Approval Voting (Journal of Politics, February 2007, pgs. 35-36), University of Pennsylvania’s Jack H. Nagel explains why exploiting non-monotonicity is not a serious threat to IRV (which he calls alternative vote):

[Exploiting non-monotonicity]…is indeed possible under the alternative vote, but the conditions it requires are extraordinarily restrictive…. Note that the kind of strategic voting required to exploit non-monotonicity under the alternative vote demands far more of voters (and organizers) than its counterpart under approval voting.  The approval voter who truncates nevertheless votes quite sincerely for his first choice, whereas the alternative-vote manipulator must put her last choice first.  Moreover, under approval voting, the act of truncating in itself does not hurt the voter’s favorite (although a resulting retaliatory spiral might), whereas the number of insincere voters under the alternative vote must be precisely calculated and controlled, or else the manipulators risk eliminating their favorite.  These drawbacks may make strategic voting under the alternative vote less benign – when and if it occurs; but they also make it, I suggest, far les probable than truncation under approval voting.

Unfortunately, no one has compared rules on the frequency of legislative electorates (simulated or actual) manipulable by [10]% of voters; the average size of conspiracy needed; the amount of information conspirators need about other rep's choices; and the risk of adverse outcomes (results worse than sincere ballots).

Concocted examples prove a possibility, not a probability.  They are no more true to life than cooked data in an ecology field study.  We know every voting rule can be manipulated.  The question then is, “Can some be manipulated more often or more easily than others?” The answer is found by statistical simulations and polling data, not by creating data to fit conclusions.  Chamberlin and others found that both sources of data showed that IRV is the least manipulable rule for large electorates.

About elections: This page presents a completion rule for policy decisions by groups of 5 to 500.  Strategic voting is expected here.  But in large elections, accidental voting cycles are likely to be more common than successful manipulations.  Simulations can compare completion rules by the “utility value” of their results in voting cycles; that measures how close to the electorate's center a rule's winning option is.  By that criterion, LOR rates below some other completion rules such as Black's combination of Condorcet and Borda.  Black's rule might be better for large elections even though it is easy and tempting to manipulate it.

Multi-winner STV is even tougher to manipulate than one-winner IRV.  Encouraging options which are similar to a projected winner can reduce its 1st preferences and lead to its elimination, but 1 of the clones will still win.  Condorcet's rule defeats that squeeze strategy and also reduces the free ride incentive in multi-winner elections.

All Loring rules use Condorcet's rule followed by Transferable Votes.

The next page shows how ranked ballots simplify the rules of order and speed up the voting.  Policy voting systems notes

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