Primer on Voting Rules
The best voting rules are inclusive, well centered and decisive.
They can make a group more popular, stable and quick.
|The tools get stronger from one voting task to the next:|
|Introduction||Tragedies of democracy: What's wrong?|
|Eras in Voting||Voting Progress: 19th Century, 20th Century, 21st Century.|
|A Small Example||Nine voters: Line up to vote, Plurality, Runoff, Two issues.|
|Chief Executive||Instant Runoff Voting: Principle, Merits, Patterns.|
|Council Elections||Proportional Representation: Principle, Merits, Patterns.|
|Funding Choices||Fair-share Spending: Old Problems, Principle, Merits. New|
|Policy Decision||Condorcet & Rules of Order: Principle, Merits, Patterns.|
After this primer shows the need for better voting rules,
the voting games will show the simple steps in each tally.
The supporting references, statistics and glossary are online. All are in the pdf for mobiles or printing in English or español.
What happens when a policy pendulum swings?
Jump to the next slide by clicking the gray link:
What's Wrong? ↓
The Northwestern U.S. was ripped apart for many years as forestry policies were reversed again and again. Hasty logging in times of weak regulation wasted resources. Sudden limits on logging bankrupted some workers and small businesses. The policy pendulum swings; it cuts down forests and species, families and towns.2
Businesses and agencies often lose money and power when a council changes hands and changes laws. Repeated reversals are a major cause of war-like politics.
Can we end such raging or silent tragedies? Better tools give real hope; we can stop the tragedies caused by the old voting tools.
Will their votes have any effect?
Our defective voting rules come from the failure to see there are different uses for voting; and these require different types of voting.
But as soon as three candidates run for one office, the situation becomes more complicated. Then that old 'yea' or 'nay' type of voting is no longer suitable.3
Sometimes what we want is not the election of a solitary official. We want to elect a whole council that represents all the voters. Then we do not need a system of dividing voters into winners and losers. Instead, we need a way of condensing them, in the right proportions, into their chosen leaders.3
Yes-or-no voting is even worse at giving fair shares of council seats, adjusting many budgets, or finding a balanced policy.
Eras in Democracy
In a district where only the biggest party wins a rep, only two big parties thrive. So the voters get only two real candidates; that is a very limited choice.4
A few of the voters who do get choices can make a council swerve from side to side.
A council majority (dark blue in picture) sets all policies and budgets. This is another battle of winner take all.
Typical Council Elected By Plurality Rule
It elects several reps from each election district. It gives a group that earns, say 20% of the votes, 20% of the council seats. Thus PR delivers fair shares of representation.6
So the side with the most seats (blue and black) forms the ruling majority; then they enact policies skewed toward their side.
Typical Council Elected By Proportional Representation
(Even a big assembly chosen by lot might use these rules to center and balance an executive committee.7)
Ensemble Elected By Central And Proportional Rules
A “compromise policy” tries to negotiate rival plans. But contrary plans forced together often work poorly, and so does the average of rival plans.
A “balanced policy” unites compatible ideas from all sides. This process needs advocates for diverse ideas. And more than that, it needs powerful moderators.
Old tally rules tend to cause one-sided results and tragedies.
An ensemble is inclusive; yet it is centered and decisive.
So it can make an organization popular, yet stable and quick.
We'll see these qualities again in the best ways to set budgets and policies.
A Small Example
Throughout this primer, we're going to show political positions in this compelling graphical way.
High taxes, great gov. services Low taxes, poor gov. services
Ms. K is the candidate nearest four voters.
L is nearest two and M is nearest three.
Candidates L and M split the voters on the right.
A mere plurality gives the winner a weak mandate.
That is the authority voters give to winners.
K is nearest four voters. L is nearest two. M is nearest three.
The two (teal) people who had voted L now vote for M.
Do votes that move count more than others? Yes, No.
This winner has the power of a majority mandate.
Only four “wasted votes” fail to elect anyone.
(Later, these voters will use a rule that asks,
“Where is our center?”
And a bigger group will use a rule that asks,
“Which trio best represents all of the voters?”)
Candidate M wins the runoff.
This photo shows voters choosing positions across two issue dimensions: left to right plus up and down. A person's position on the first issue does not help us guess their position on an independent issue.
Which leaves more wasted votes, plurality or runoff? Which gives the winner a stronger electoral mandate?
Kay wins a plurality. Em wins a runoff.
How does it work? You rank your favorite as your first choice,
and rank backups as your second choice, third and so on.
Then your ballot goes to your first-rank candidate.
If no candidate gets a majority, the one with the fewest
ballots loses. Then there is another round of counting.
Here is an analogy: Each candidate puts out a box. A voter puts his ballot in his favorite candidate's box. The ballots are counted.
If the box gets a majority of the ballots, it wins. If not, the voter moves his ballot to another candidate's box. Or, he waits, hoping others will move their ballots to his favorite box.
To break that deadlock, we have a rule: If a round of counting ballots finds no winner, the box with the fewest votes is eliminated. Its ballots go to each voter's next backup choice — probably a candidate with similar views and more popularity.
These transfers make voters condense into large groups supporting strong candidates. Ballots are counted again to see if any candidate gets half of the current top ranks.
In practice, each voter ranks the candidates as 1st choice, 2nd choice, 3rd etc. Then election officials move ballots between boxes or a computer tallies them.
In a South Korean presidential election, two
progressives faced the aide to a military dictator.
The progressives got a majority of the votes but split
their supporters. So the conservative won under
a plurality vote-counting rule. These rules elect
whoever gets the most votes; 50% is not required.
The winner claimed a mandate to continue repressive policies. Years later he was convicted of treason in the tragic killing of pro-democracy demonstrators.4
With Instant Runoff Voting, ballots for the weaker progressive could have transferred to help elect the stronger one.
The U.S. also has seen major elections in which two candidates on the left split their voters or two on the right split theirs. Sometimes this increased our national tragedies. (Can you name such an election and its tragic results?)
From five factions to one majority.
In some places, people call this Rank Choice Voting, Preference Voting or the Alternative Vote.
IRV lets you vote for the candidate you really like. And even if that option loses, your vote isn't wasted; it goes to your next choice.
In the first seminar group, 5 voters elect B to power,
while 4 people waste their votes on a loser, J.
In the last seminar, 8 voters elect M, but 3 of those votes are wasted in a surplus that has no effect.
A minority with 11 voters gets majority power with 2 reps. (But if it were spread out evenly, it would get none.)
Now a majority gets two reps and a minority gets one.
That is, 60% of the vote gets you 60% of the seats,
not all of them. And 10% of the vote gets you 10%
of the seats, not none of them. These are fair shares.
Those Chicago Republicans were usually moderates. So were Democratic reps from Republican strongholds. Even the biggest party in a district tended to elect reps who were more independent. They could work together and make state policies more moderate.4
(The transferable-vote game shows one way to get PR — which is also called Fair Voting, Proportional Voting, Full Representation, or Fair Representation.
The number of women elected rose from 21% to 29%. The number of native Maoris elected rose from 7% to 16%, which is almost proportional to the Maori population.5 Voters also elected 3 Polynesian reps and 1 Asian rep.
New Zealand and Germany elect half of their MPs by list PR and half of them in single-member districts. Their districts elect few women; but in the same election, the PR lists elect three times more women.
In every one-seat district, a party's safest nominee is likely to be a member of the dominant sex, race, etc. That adds up to very poor representation of all others.
PR leads each party to nominate a balanced team of candidates to attract voters. This promotes women.6 A team may have class, ethnic and religious diversity. And that gives us diverse reps to approach for help.
This credible threat made some parties decide that job experience was not as important as gender balance. So they dropped some experienced men to make more room for women on the party list. And they won.7 Now they are incumbents with experience, power and allies.
SMDs elect reps with a wide range of vote totals. But PR requires the same total for each rep. But PR requires the same total for each rep. So any majority of reps really stands for most voters. That helps its policies match public opinion better.
If those urgent needs overwhelm us, we neglect the essential needs, the structural roots of our problems. We often get bad results from poor policies, due to poor representation, caused at the root by bad voting rules. We might agree, helping voters control government is now an urgent need.
The countries with the best voting rules get the best quality of life, as measured in their international scores. Wouldn't you like the best results for your country? (and for your town, school, club or company?)
Proportional Representation distributes council seats fairly.
In the same way, voting can distribute some spending power fairly.
Fair shares give minority voters some power.
Even in groups that lack competitive elections, some members compete over money to fund their projects. So some may connive to capture part of the budget. This injustice can push others to rebel or just leave. They have a right to fair shares of decision power.
A bad election rule gets even worse at setting budgets: It's not “cost aware,”; so it often funds the most costly item and cuts a bunch that get many more votes per dollar. To win this bad tally, load various items into one proposal. Keep raising its cost if that attracts more votes.
Consensus would struggle to weigh dozens of desires, of varied cost and priority, from dozens of overlapping groups.
Many empty hands Fair Shares
The old way to set budgets blurs responsibility. Take deficit spending: Progressives may say too much is spent on big weapons and corporate subsidies; conservatives often blame the money spent on health, education and the environment. Every rep can claim, “I didn't spend too much.”
Protecting the environment is popular with both conservative and progressive voters. Reps don't dare attack it openly. So, to pay off some campaign gifts from corporate sponsors, reps slyly starve agencies that enforce environmental laws. Budget cuts have also starved OSHA, ATF and the auditors of corporate tax returns.
“Lower but constant funding is more productive than a roller-coaster budget that might average far more.” Alvin Trivelpiece, director, Oak Ridge National Laboratory
The Texas Super-Conducting Super Collider was a multi-billion dollar project in the 1980s. This effort to build the world's largest cyclotron was supported by a majority in Congress for a few years... then dropped. The only thing built was a “billion-dollar hole in the ground.”
Members might be more cautious about starting vast projects if they could not spend the opposition's share of the budget. And they should have the power to finish their projects with their own share.
Each rep voted yes or no to a huge “omnibus” bill. It held hundreds of earmarks, some good, some bad. This budget system made it hard to prove which reps are wasted money.
At their best, earmarks let a rep use federal money to fund vital local projects that only locals see the need and chance to do. But there is a better, more responsive and democratic way to select projects, Participatory Budgeting.
Twin Oaks Community started its annual Trade-Off Game in the 1970s. To make it interesting, the rules change a little from year to year — it's a rare, long-term effort to test, improve, and retest voting rules. Many games have had some money to spend on One-Time Resource Allocations, OTRAs. These have ranged from $15 of music to $4,000 scholarships. In 1996, a proposed scholarship got many surplus votes. Those were wasted votes because they had no effect. So the next year, some supporters chose not to waste a vote on this sure winner. It lost! They saw the need for a voting rule that could never waste surplus votes.
In Chicago, a top alderman first gave his discretionary fund to PB in 2010. It was a popular success. But due to an old plurality rule, similar to bloc vote, more than half the votes were 'wasted': a majority of votes went to losers.2
Even the winning votes were wildly unequal. Each vote for the playground was worth $501. But each vote for the bike racks was worth only $31. That's too unfair; we can do better. We can give every voter the power to guide a fair share of money, with Proportional Voting: PV for PB.
Voting reforms are hard because unfair rules have become entrenched by centuries of use. But PB is still young, so we have a rare opportunity to introduce better voting rules now — voting rules that are more expressive and fair.
That is, 60% of the voters spend 60% of the money,
not all of it. A project must show it is it is a common good worth group funds by getting grants from many voters
So we let a voter fund only a set fraction of a project.
How does it work? Like IRV: You rank your choices.
Then your ballot gives grants to your top choices. And a tally of all ballots drops the least-funded project. This repeats until all projects still in the race are fully funded.
(The voting games will make the details easy to grasp.)
Each proposal needs support
from a substantial group.
Every neighborhood and interest group controls its share of spending power; no one is shut out. This cuts the incentive for a group to dominate others. So it makes (hidden) empires less profitable.
If a plurality spends all the money, the last thing they buy adds little to their happiness. It is a low priority. But that money could buy the high-priority favorite of a large minority; making them happier.
In economic terms: The “social utility” of the money and goods tends to increase if we each allocate a share. Shares spread the opportunities and incentives too.
In political terms: Fair shares earn wide respect, as we each help big minorities to fund some projects. So our budget appeals to more people.
Each budget level of an item is like a project:
To win, it needs to get a base number of votes.
It gets a vote when a ballot pays a share of the cost
up to that level or higher. cost / base = 1 share = 1 vote
If more ballots divide the cost, each of them pays less.3
I only pay up to a level I voted for and can afford.
One at a time, the weak ones lose and the money moves. The item that gets the fewest votes for its current top level, loses that level. Any money you gave it flows to your highest rank that lacks your money. This repeats until the remaining top level of each item is fully funded - by a strong base of support.
1) In FS, the proper name for a base of support is a “support requirement” for each budget level.
• If a level gets more than enough votes and money, a share of the surplus goes back to each donor, as in STV.
• The voting game shows how to give your favorite two votes and lower choices less than one.
My second choice lost; did it waste any of my power?
My third choice got 50 votes, so I paid only 2% of the cost, half a vote. Were there any surplus votes? Did I waste much power by voting for this sure winner?
Fair shares can set the budgets of departments too.
Each “line item” starts with most of its past budget.2 A voter may write-in and rank higher budget levels for a department.
2) Each item could start with all of its past budget:
A voter ranks the ones he is most willing to cut, with his share of “negative dollars”. Twin Oaks Community set their base number at 55% when using FS to make controversial budget cuts. (A second poll could let voters try to restore and increase funding to their favorite items. This has not been tested due to the time cost and perhaps increasing adversarial relationships.)
Each agency starts with % of its current budget.*
A rep may refill only a limited share of each budget.
So it takes many reps to refill one, and more to raise it.
You repeatedly adjust your grants, causing and countering budget changes, until a timer stops the voting.
* To vote less than about % to basic services, such as
the police or public health, would be “stealing a free ride.”
BRV lets a majority reduce their grants to agency X. This undercuts a minority's grants to X. So, to maintain the total for X, the minority must give it bigger grants. Then the majority reduces theirs again, and this cycle repeats. With BRV, nobody apportions the budget as they sincerely want it. In contrast, the fair-share rule above gives all large groups positive power to fund their favorites.
Here is a second Pairwise test with the same voters.
K is nearest four voters. L is nearest five voters.
She has won majorities against each of her rivals. So her position is the “Condorcet winner”, the one policy judged to be best by every majority of voters.
Thus a Condorcet Tally picks a central winner.
For example, it can elect a moderator to a council.
And it can set the 'base of support' in Fair-share Spending.
Is it likely to elect diverse reps? Yes, No.
L is nearest six voters; M is nearest three.
The sports analogy is a “round-robin tournament.” A player has one contest against each rival. If she wins all of her tests, then she wins the tournament.
Option J tops option D if most voters rank J above D.
Each ballot's rank of J relative to D concerns us.
The numbers of first-rank votes do not.
If another rule picks a different winner our Condorcet winner ranks higher on most ballots. So it wins a one-against-one majority over that other rule's winner.
(More merits of the Condorcet or “Pairwise” rule...)
Everyone helps choose our center.
So the Condorcet winner is well balanced and widely popular:2 Most centrist and progressive voters like it more than any conservative policy. At the same time, most centrist and conservative voters like it more than any progressive policy. All sides can join to beat narrowly-centrist policies.
A Condorcet Tally can elect a central chairperson and a vice chair to hold the powerful swing votes on an Ensemble Council. They compete for support from voters left, right and center. So they have strong incentives to balance a council's process and policies.
Proposed policies compete for high ranks from all members, but the chairs often cast the key votes.
Condorcet tallies elect about one out of four reps. Proportional Representation elects the other reps.
But M might lose to someone less moderate in her party's primary — the most challenging election she is likely to face.3
The old plurality rule is the easiest to manipulate. (Borda and point voting are often susceptible too.) But the Pairwise winner, L, doesn't change in this case. Proportional Representation or (post-election) proxy votes avoid even the common bias due to housing patterns.4
Now K has 3 votes. L has two. And M has four.
Voting rules that give fair shares of seats and spending also reduce the payoffs to those who bribe the biggest party. It can no longer seize more than its share of reps or money.
|2||Original Bill, the main motion|
|1||Bill with Amendment One (a free-rider?)|
|7||Bill with Amend. Two (a killer amend.?)|
|6||Bill with Amendments One and Two|
|3||Postpone for 1 days|
|4||Refer the Bill to a Committee|
|5||No Change in the status quo|
Other meetings discuss rival options all at once; yet many people don't express their backup choices. So similar options split supporters and hurt each other. Then a minority pushing one option can appear to be the strongest group. Even worse, a person with a well-balanced option but few eager supporters might drop it.
Committees sometimes choose parts of a policy. They often allow other voters only a yes-or-no choice. A yes-or-no process may require a committee report only two options for all members to choose between.
Rigged voting often builds a bad policy and hostility.
The best rules avoid all those problems by letting voters rank closely-related options on one ballot.
Benefits and Costs
Which is more stable and quick?
Does your car have an 1890 steering tiller or a new, power steering wheel? Does your organization have an 1890 voting rule or a new, centered and balanced rule?
Today's drivers need the skill to use power steering — but they don't need the math or logic to engineer it. Same with voters and voting rules.
Many groups adopt a standard book of parliamentary rules; then they amend it with their own “special rules of order”. So they own a modern vehicle for making their decisions more popular, stable and quick.
The official rules model the goals and methods for shared decisions. They teach some patterns often followed by coworkers, friends and neighbors.
Fair rules make cooperation safer, faster and easier. They favor people and groups who tend to cooperate, and may lead others to cooperate more often.
Politics are more principled and peaceful when all the rules tend to help us find fair shares and central majorities. These may reduce political wars and fears in a group, helping it embrace more freedom and diversity. Then the group's size and resilience may increase.
So better rules can help us build better decisions, plus better relationships. Both will please more people. Someone whose income or self-worth comes from war-like politics might not be pleased. But fair rules most likely tend to raise happiness on the whole.
Public campaign funding in Maine and Arizona lets reps spend less time with rich sponsors and more with voters. One plan would gives each voter $50 of vouchers to donate. Such small, nameless donations or FS can cut corrupt paybacks.3
One-seat districts let the campaign PACs pour floods of money into the few tossup districts and thus win most of the swing seats. PR has close races in many multi-seat districts, forcing the PACs to spread-out their money into most districts.
Ballot access laws make it hard for minor parties to get nominees on the ballot. The two big parties make those laws largely because they fear spoiler candidates. Better voting rules such as IRV can calm that fear.
Sabbatical terms make the current rep run against a former rep returning from sabbatical. The voters get a real choice between two winners. Each has a record of what they did in office. Plurality rule would tend to make the current and former reps both lose by splitting their party. But these rank-voting rules do not split parties. A sabbatical might pay the rep to work with others from all parties on a service project, a bus tour and a rural retreat.
Policy juries or initiatives can give voters more choices and power through ranked-choice ballots and Condorcet tallies. They should set the political rules and ratify the laws about lobbyists, PACs, campaign ads and salary for reps. But minority rights to ballots, reps and funds need constitutional protection from the majority of the day.
The data make it clear: Advocates for education, health care, a clean environment and a clean government should all work for better voting rules. Donors should too.
If we are overwhelmed by urgent needs, we neglect the essentials, the structural roots of these problems. We continue to get bad public policies, due to bad representation, due to bad election laws.
Your work goes on giving to a school, club or town.
Election campaigns cost a lot all at once. If you win control, you can help all issues for two years.
Reform campaigns cost no more than elections. A win affects the whole council for many years. Your work keeps giving to a school, club or town.
Give fair representation to all major groups. So the council enacts laws with real majorities.
Why Take VotesGroups with little time and many issues or competing interests, often end a discussion by asking for votes not consensus. Their methods of discussion and of voting each affect the quality of their decisions and the group's morale.
The secret ballot can protect voters from many types of coercion.
The Condorcet policy can please most members best; it is not biased for any group or the current policy. It also does not need to favor the status quo, except bylaws.
Fair-share Spending can give fair shares of power. Inclusive yet fast, it doesn't let one member block action. It is co-operative decision making, not individual nor hierarchical, not consensual nor adversarial. Multi-winner rules are less about blocking rivals, more about attracting allies.
One set of policies sometimes cannot suit two groups with opposing values.
Moving to a better place is the surest way to get the policies you want.
This is often called “voting with your feet”.
That is practical when you have the freedom to move and diverse destinations to choose among. Such diversity is more likely when culture and technology give places economic independence through “local self-reliance”.
Even when you can't move to a better city or country, you may still avoid willful authoritarians. Build your democratic groups with fair egalitarians.
Democracy improves in eras such as The Enlightenment. Many people restrained blind faith, obedience and ideology. They expanded our knowledge of the universe and understanding of life through rational, skeptical, empirical thinking.
Many people are excited to learn that voting does not have to mean “winner take all.”
The best voting rules strengthen the ballots for voters.
This page shows different voting uses
Learn more in this e-book, Accurate Democracy. Then build support in your school, club or town with FairVote, The Center for Voting and Democracy.
Steps toward accurate democracy include:
This website has sim games and handouts,
This text is © CC BY-SA 3.0, so edit it as you will and add your own slides for other topics. For example, U.S. voters need concise statements of the principles and benefits in non-partisan redistricting, as practiced in Iowa, and public campaign funding, as practiced in Arizona, Maine, or North Carolina.
You may want to skip some topics or change the wording to suit an audience. For legislators you might change “voter” to “rep” or “member” and you would do the opposite for a direct democracy.
Thanks to Steve Chessin for writing the original version of the “elevator pitch” for Proportional Representation. He, Terry Bouricius, and Zo Tobi each wrote quick pitches for Instant Runoff Voting which were the basis for the IRV slides above. Overall editors include Tree Bressen, Cheryl Hogue, John Richardson, and Rob Richie. Many others have contributed ideas and writing.
BooksThis primer is part of a free booklet for printers or screens. It has the voting games, colorful graphics from both PoliticalSim™ and the budget voting games, data to compare nations and references. A few hard cover copies are available for college libraries.
This page showed the need for better voting rules and their merits. The next page, voting games, show the simple steps in each tally and how they meet their goals.
After that, you may want to read the one-page introduction to each of the six voting tasks. These tell how a task is like and unlike other uses of voting, what it must do, stories of tragedy and success, the best rule's name, its ballot and its main merits.
Accurate Democracy is organized by uses of voting:
|Electoral Systems||Legislative Systems|
Ads versus info
Some people want a better Chinese translation.
And some people want a better Arabic translation.
Please help them.
Dos voluntarios han hecho traducciones al español (Spanish):
Democracia con precisión y Democracia Certera. ¿Cuál te gusta?