Voting Rules for

Different uses for voting need different types of voting.

Voting rules for setting policies; Condorcet rules

Trading Policy Votes

Introduction to Condorcet rules, chapter contents

A rep can increase her power on issues she cares about by trading away votes on other issues. This creates a barter economy for setting policies. It gives even the smallest minority faction a chance to bargain. So it spreads power and increases satisfaction, at least on core issues.

It is superficially easier to trade the yes's and no's of plurality ballots than the rank numbers on preference ballots. But is it easier when the plurality ballots require a series of votes on amendments and other motions? The final bill might be amended into something very different from what you bargained for.

The preference ballot lets the traders agree, "I'll rank all versions with your amendment above all versions without it if you will do the same for my amendment.

Bluffing, pretending to mildly oppose whatever a potential trading partner favors, is common. By pretending to "change" my vote (to just what I sincerely wanted) I get something for nothing. Of course the mere possibility of such behavior increases suspicion and cynicism.

Some people find trading partners; others don't - so the distribution of power becomes uneven, as intended, but also unfair. One person might gain 3 or more votes on an issue while another, who cares about it just as much, gets only 1 vote.

Trades can even allow bidding in fractions of a voter's weight. One rep might, for example, bid to trade half a vote (an abstention) on a hot issue for a whole vote on an issue with less demand. She could still trade the other half, reversing her vote to gain another trade.

Even when trades are public, the effects of a rep's votes are less clear and less accountable to the voters.


A computer-based auction system can make trades easier and safer. The software ballot assistant could be a key to vote trading for policies.

The simplest case has three groups, Left, Center, and Right setting policies for two issues: School, and Health. The options proposed for the School issue are labeled A and B. Y and Z are proposals for the Health issue.

Table I shows each faction's size and preferred School and Health policies. The bold letters indicate the Left voters ardently desire the A policy for School while the Right strongly desire the Z policy for Health. Each faction is willing to trade votes on other issues to win their major issue.

Table I, Preferences on Single Issues
Voters Faction School Issue Health Issue
4 Left A Y
2 Center B Y
4 Right B Z

When Left and Right are about the same size, the Center faction holds the swing votes. So their choice would win with sincere votes under any fair voting system if the issues are decided separately. But if the voters have a choice of policy packages combining School and Health options, then vote trading can be automatic.

Table II  Preferences on Packages
			Package Preferences	
Faction  	First	Second	Third	Fourth
4 Left AY 	AY	AZ	BY	BZ
2 Center  	BY	BZ	AY	AZ
4 Right  	BZ	AZ	BY	BZ

Table III   Condorcet Pairwaise Tally
AY	-	8/2		
AZ	8\2	-	8\2	8\2
BY	4/6	8/2	-	
BZ		8/2		-

Combining issues leads to an combinatorial explosion in the number ballot items a voter must rank. So the Ballot Assistant is a great aid in allowing packages for vote trading.

Table IV   Packages to Rank
Issues			Policies		
		2	3	4	5
2		4			

* Ballot assistant helps reps vote on a very large list of options. This allows them to combine several policy decisions into one package vote.

Suppose you are in the majority in choosing policy C on issue One. You are in the minority in choosing policy D on issue Two. And you rank policy Two D above all versions of issue One.

The opposition party is in the minority in choosing policy B on issue One. They are in the majority in choosing policy C on issue Two. And they rank policy One B above all versions of issue Two.

A utility rule such as Borda's can find the combination of One B and Two D -- but it is easily manipulated. Can Condorcet's rule find the combination of One B and Two D ?

What is the simplest case? If we have only two factions, then one is a majority and they get whatever combination of policies they vote for. So all revealing examples have at least three factions. Red, Blue and Green will label the parties.

Issue I has proposals A, B and C. Issue II has K, L and M. On issue III the proposals are X, Y and Z.

B, L, and Y are the Condorcet winners (CW) on the three issues. But most voters prefer the CKZ package. It wins the one-on-one comparison with BLY.

Even with Assisted Ballots, reps can be overwhelmed if too many proposals are allowed on one ballot. This puts a very low limit on the number of issues that can be combined into packages.

In American legislatures a rules committee decides whether a proposed amendment is germane to a bill and so may be attached to it. Its members will lose some power if a Condorcet rule lets the other reps pare away free-rider amendments. But its members might gain power if they can combine issues and make packages possible.

A combination of several issues, each with several options, usually will make strategic voting conspiracies more difficult.

z_future.htm speculates on a way of ranking priorities that discourages vote trading as it gives a voter 1 vote on an average priority, extra weight on his top priority, and less than 1 on low priorities.  

Next simulations of several voting rules give us data about how often they can be manipulated. Data about manipulation

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