Different uses for voting need different types of voting.

 Voting systems and election rules for Accurate Democracy

Primer on Voting Rules

 Introduction to voting systems, chapter contents

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:
IntroductionIntroduction Tragedies of democracy: What's wrong?
PR Representatives and DelegatesEras in Voting Voting Progress: 19th Century, 20th Century, 21st Century.
IntroductionA Small Example Nine voters: Line up to vote, Plurality, Runoff, Two issues.
IRV 1 Side WinsChief Executive  Instant Runoff Voting: Principle, Merits, Patterns.
PR Representatives and DelegatesCouncil Elections  Proportional Representation: Principle, Merits, Patterns.
Project DistributionFunding Choices  Fair Share Voting: Old Problems, Principle, MeritsNew
Pairwise CenteringPolicy Decision Condorcet & Rules of Order: Principle, Merits, Patterns.
   Benefits and Costs.    Prints.    español.   
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.



Tragedies of Democracy

These tragedies were caused by voting rules often used by countries and towns, co-ops and corporate boards.
Clear cut mountain

What happens when a policy pendulum swings?

Jump to the next slide by clicking the gray link:
  What's Wrong? ↓

Old ways of adding up votes fail to represent large groups in many places.  In the USA, North Carolina had enough black voters to fill up two election districts. But they were a minority spread out over eight districts.  So for over 100 years, they won no voice in Congress.  As voters, they were silenced.1

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.

What's Wrong?

Voters waiting waiting, by Kiichiro Sato

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.

We all know how a group can vote on the simplest type of issue: A question with only two answers is voted 'yes' or 'no'. For such a question, the yes and no votes are enough.

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

The 1800s: Winner-Take-All Districts lead to Off-Center Councils

Some English-speaking countries still count votes by England's old plurality rule.  It elects only one representative from each district; and winning it does not require a majority.  It merely elects who­ever gets the most “yes” votes. 

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

It gets worse: a district's bias normally makes it a 'safe seat' for one party. So most voters get no real choice.5

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.

 Plurality election
$  $  $  LAWS   $  $  $

Typical Council Elected By Plurality Rule

1900s: Fair-Share Representation leads to Off-Center Majorities

Proportional Representation was developed around 1900 to end some major problems caused by plurality rule.  Most democracies now use “PR”.

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

This leads to broad representation of issues and opinions.  But usually there is no central party (C in picture). And the two biggest parties normally refuse to work together.

So the side with the most seats (blue and black) forms the ruling majority; then they enact policies skewed toward their side.

 Proportional Representation
$     $  $  LAWS  $  $      $

Typical Council Elected By Proportional Representation

2000s: Ensemble Councils lead to Broad, Centered Majorities

New ensemble councils will elect most reps by Proportional Representation, plus a few by a central rule ( C  in picture).  Later slides show how a voting rule can pick winners with wide appeal and views near the middle of the voters.  Its winners are thus near the middle of a Proportional council.
 So they are the council's powerful swing votes. 
Most voters in the winners' wide base of support don't want averaged or centrist policies.  They want policies to combine the best suggestions from all groups.

(Even a big assembly chosen by lot might use these rules to center and balance an executive committee.7)

 Mixed Member Proportional MMP

Ensemble Elected By Central And Proportional Rules

A soapbox supports the shoes of a speaker.       Democracy Evolves       A TV shows the face of a speaker.

A “centrist policy” enacts a narrow point of view; it excludes other opinions and needs.
A “one-sided policy” also ignores rival ideas. 

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. 

A broad balanced majority works to enact broad, balanced policies.  These tend to give the greatest chance for happiness to the greatest number of people.  Excellent policies are a goal of accurate democracy.  Their success is measured  by data on a typical voter's education and income, freedom and safety, health and leisure.7

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

Nine Voters

Let's think about an election with nine voters whose opinions range from left to right.  The figures in this picture mark the positions of voters on the political left, right or center — as though we asked them, “If you want high-quality government services and taxes like Norway or Sweden, please stand here.”
“Like Canada?  Stand here please.  Like the USA?  Stand here.  Stand over there for Mexico's low taxes and government.”

Throughout this primer, we're going to show political positions in this compelling graphical way.

Nine voters spread out along an issue.

 Nine voters

High taxes, great gov. services Low taxes, poor gov. services

Jump to the next slide by clicking the gray link:    Plurality ↓

Plurality Election

Three candidates stand for office.  A voter
likes the one whose political position is nearest. 
So voters on the left like the candidate on the left.

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.

Does a majority (over half) elect one?   Yes, No.
Who wins the plurality or largest share?   K, L, M.
Who wins the second largest share of votes?   K, L, M.
Answers: Mouse over a question, but do not click.

A mere plurality gives the winner a weak mandate
That is the authority voters give to winners.

By plurality rule, the one with the most votes wins.

 Plurality election

K is nearest four voters. L is nearest two. M is nearest three.

Runoff Election

Who wins a runoff between the top two candidates?   K, M.

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.

Runoffs practically ask, “Which side is stronger?”

(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?”)

In a runoff, the top two compete one against one.

 Runoff election

Candidate M wins the runoff.

Politics in Two Issue Dimensions

Voting rules behave the same even when opinions do not fit neatly along a line from left to right.1

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.

“Please step forward for more regulation of __. 
Please a step back if you want less regulation. 
Take more steps for more change.”

Which leaves more wasted votes, plurality or runoff? Which gives the winner a stronger electoral mandate?

Seventeen voters spread out along two issues:
more or less regulation ↕ and taxes for services ↔

 Voters in 2 Issue Dimensions

Kay wins a plurality. Em wins a runoff.

Chief Executive

The Goal of Instant Runoff Voting is this:

A majority winner
from a single election.

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. 
Your ballot stays with your favorite if she advances. 
It moves to your backup if your favorite has lost.
This repeats until one candidate gets a majority.

Instant Runoff Voting, a Tally Analogy

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.

Some Benefits of Instant Runoff Voting are:

  • A majority winner from one election, so no winners with weak mandates and no costly runoff elections.
  • Higher voter turnout, it often drops in runoffs.
  • Less campaign spending, it often goes up in runoffs.2
  • Less divisive campaigns and attack ads, as a candidate tells rival factions why she is their best backup choice.3
  • No hurting your first choice by ranking a backup, because it does not count unless your first choice has lost.
  • No lesser-of-two-evils choice, because you can mark your true first choice without fear of wasting your vote.
  • No split-vote worries for a faction, as votes for its weakest candidate move to each supporter's backup choice.

Plurality Voting Patterns

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?)

Instant Runoff Voting Patterns

From five factions to one majority.

 Four IRV pie charts

 1) Ms. Violet loses.  Her ballots go to each voter's next choice.
2) Ms. Blonde loses.  Her ballots move.
3) Ms. Green loses.
4) Ms. Carmine loses.
IRV elects leaders in cities large and small: London, Melbourne, Minneapolis, San Francisco, Sydney and others.  Students use it at Duke, Harvard, MIT, Rice, Stanford, Tufts, UCLA, Cal Tech, Carlton, Clark, Cornell, Dartmouth, Hendrix, Reed, Vassar, Whitman, William and Mary, The Universities of: Cal, Il, Md, Mn, Ok, Va, Wa, Wi, and more.

In some places, people call this Rank Choice Voting, Preference Voting or the Alternative Vote.

A picture in the transferable-vote game illustrates individual ballots moving.

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.

Council Elections

3 Single-Winner Elections

A class of 27 wants to elect a planning committee.  Someone says, “Elect a rep from each seminar group.”

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.)

Proportional Representation

A better suggestion says, “Keep the class whole.
Change the definition of victory from half of a small
seminar to a quarter of the whole class, plus one.”
So 3 reps must get 3/4, not just a plurality.
More effective votes mean fewer wasted and a stronger
mandate for council decisions.

Now a majority gets two reps and a minority gets one.

The principle of Proportional Representation is this:

Majority rule,
with representation for political minorities,
in proportion to their votes.

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.
    How does it work?  There are three basic ingredients:
  • We elect more than one rep from each district.
  • You vote for more than one; you vote for a list.
    Parties offer their lists to us, or we each list our favorites.
  • The more votes a list gets, the more reps it elects.

Some Benefits of Proportional Representation:

  • Fair shares of reps go to the competing groups. so
    Diverse candidates get a real chance of winning. so
    Close races for swing seats are on most ballots, so
    Real choices for the voters and high voter turnout.1
  • Women get elected about three times more often.2 so
    Majority rule improves — also by few wasted votes, real choices, turnout and reps with equal support. so
    Policies match public opinion better.3

Fair Shares and Moderates

Chicago now elects no Republicans to the state House, even though they win up to a third of the city's votes.  But for over a century it elected reps from both parties.  The state used a fair rule to elect 3 reps in each district.  Most districts gave the majority party 2 reps and the minority 1.  So both parties courted voters in all districts.

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.

New Zealand switched in 1996 from Single-Member Districts to a layer of SMD within Proportional Representation.  A small one-winner district exaggerates local issues and alliances.  Proportional Representation frees voters from the confinement of small districts; so they can elect reps with thin but widespread appeal.

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.

Print editions of this primer include statistics on the effects of PR on election of women, on policies and on the quality of life.

Why Elect Women

Does Proportional Representation elect more women?

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.

Some leading women spoke of starting a new party in Sweden which uses PR. Under plurality rule, a big new party splits their own side, so it loses. But Fair Rep gives every big party its share of seats.

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.

Voting Rules and Policy Results

A woman in a multi-winner race is not so much running against a man or an incumbent. She is more often seen as running for her issues. Also, most “women prefer to compete in teams,” not solo.8

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.

Shares of votes equal fair shares of seats.

Consequences: Legislatures with fewer women tend to give less attention to health care, child care, education, and other social needs. Run-down schools and city hospitals are one blight; a class of citizens with inferior education and health are another.9

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?)

Funding Choices

Fair Shares to Buy Public Goods

Electing reps is the most obvious use of voting rules. Rules to set policies and budgets are just as important. In fact, they get used more often than election rules. They may be the only votes in a more direct democracy, using initiatives, proxies, or councils chosen by lot.1

Proportional Representation distributes council seats fairly.
In the same way, voting can distribute some spending power fairly.

Democratic rights progress 
Each step makes a democracy more fair, thus accurate, popular and strong.
Fair Rep Voting for rich men, poor men, “colored” men, women.
Fair Rep Proportional Representation for large political minorities.
Projects Fair Share Voting by big groups of voters or reps.

 Fair shares mean minority voters also have some power.


Fair shares give minority voters some power.

A Pattern of Unfair Spending   

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

Many empty hands Fair Shares

Old Budget Patterns      

Lack of Transparency and Accountability

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.

Old Roller-Coaster Budgets

“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.

Local Control of Central Funds    

The U.S. Congress let a single rep “earmark” funds for pet projects.  In 1994, the 4,000 earmarks cost us $23 billion.  Ten years later, the 14,000 earmarks cost us $45 billion.

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.

Participatory Budgeting: PB is a big step up for democracy. It lets local meetings research, discuss and vote how to spend part of a city's budget.  In South America, it spread from 1 city in 1989 to several hundred today.  The World Bank reports that the Participatory Budgeting or PB process tends to raise a city's health and education while reducing corruption.1

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.

The principle of Fair Share Voting is this:

Spending power for all,
in proportion to their votes.

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.)

Merits of Fair Share Voting

For Picking New Projects

  • FS is fair to a project of any price and to its voters:
    It takes a costly grant to vote for a costly project.
    Your ballot's money can help more small projects.
    So give top ranks to the projects you feel offer the most joy per dollar.
  • FS cuts wasted votes the way IRV does:
    Your votes move from losers to backup choices;
    So rank your true top choices without fear of wasting a vote:
    It's not a waste to vote for a likely loser or a sure winner.
    There's little incentive for tactical nominations or voting:
    Less worry that similar proposals will split their voters.
  • All of these points raise voter turnout; all give more votes, support, and legitimacy to the set of winners.
  • After discussion, one poll quickly sets many budgets. It reduces agenda effects such as leaving no money for the last items or going into debt for them.
  • Fairness builds trust in group spending, which can raise support for more of it — and less spending at the extremes of individual and central control.

For Funding Agencies

  • This does not give minorities too much power: A majority spends most of any fair-share fund. They set the policies that direct each department. They may end any program before the voting starts.
  • FS smoothes roller-coaster budgets that hurt efficiency. It stops starvation budgets designed to cause failure.

For Votes by Elected Councils

  • A member can waste only her share of the fund. Voters can see a rep's grants to each project, tax cut or debt reduction and hold her accountable.
  • FS gives some power to reps in the opposition, so votes to elect them no longer feel like wasted votes.
    This can increase voter turnout.
  • It lets sub-groups pick projects; so it's like federalism, but without new layers of laws, taxes and bureaucracy. And it funds big groups even if they're scattered.

Fair Share Voting for Participatory Budgeting

  • Fair Share Voting is fair
    Each ballot controls the same number of dollars.
    The largest group can't control more than its share.
    Minority groups can control their shares of money.
    Voters know that their votes count.
  • Fair Share Voting is cost-aware
    Funds the projects with the lowest costs per benefit     (Benefits are measured by numbers of votes.)
    Fair to less-costly projects and their supporters
    More voter satisfaction per dollar spent
  • Votes for unpopular projects are not wasted, and votes for popular projects cost less
    Less incentive for tactical voting
    More support for the winning set of projects
    A stronger mandate for the final decision
  • With these benefits, we can hope to:
    Increase voter turnout and satisfaction.
    Encourage more officials to entrust PB with
        more money in more cities.
Twin Oaks Community in Virginia has experimented with Participatory Budgeting methods for over 35 years. In 2007 they first set budgets for projects by Fair Share Voting. In 2013 they used it to adjust ongoing budget areas.

Fair Share Voting Works This Way

 Several hands giving dollars to several projects.

Each proposal needs support
from a substantial group.

In a citywide vote, each neighborhood or interest group funds a few school, park or road improvements.  The city's taxes then pay for the projects as the School, Park, and Road Departments manage the contracts.

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.

Adjusting Budgets

You may write-in and rank budget levels for an item. Your ballot may pay only one share of a budget level. Often, it can afford to help most of your favorite items.

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
You only pay up to a level you 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 item two votes and lower choices less than one.

One Voter's Ballot: A group with 100 members set their base number at 25 votes.4 My first choice got just enough votes, so my ballot paid 4% of the cost.   100% / 25 voters = 4%.

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 itemstarts 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.)

Fair Share Voting Slideshow:

“Proposing a New Voting Method
For Participatory Budgeting”

HOT!  The presentation about Fair Share Voting
from North America's first PB Conference!
English: Open Office slide show, Printout (PDF).
Español: Open Office diapositivas, impresora.
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Condorcet Test Number Two

The nine-voter Runoff above was a one-against-one or “Pairwise” contest between the policy positions by candidates M and K.  Five voters preferred M's policy position over K's.

Here is a second Pairwise test with the same voters.

K's position loses this one-against-one test.
Candidate L wins by five votes to four.

(Each person votes once with a ranked-choice ballot.  There are several ballot styles.)

 Condorcet contest 2

    K is nearest four voters. L is nearest five voters.

Condorcet Test Number Three

Candidate L wins her next one-on-one test also. She even got one “surplus vote” more than needed.

She has won majorities against each of her rivals. So her position is theCondorcet winner”, the one policy judged to be best by every majority of voters.

Could another person top candidate L?   Yes,  No.
Hint: Is anyone closer to the political center?   Yes,  No.
Who is the Pairwise winner on page 9?   K,  L,  M.

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 Voting.
Is it likely to elect diverse reps?     Yes,  No.

 Condorcet contest 3

L is nearest six voters;     M is nearest three.

The goal of a Condorcet Tally is this:

Majority victories
over every single rival.

The winner must top every rival, one-against-one.

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.

Each voting test sorts all of of the ballots into two piles.  If you rank option J higher than D then your ballot goes in the pile for J.  The option with the most ballots wins that test.  If an option wins all of its tests, then it wins the election. (If none does, IRV can pick one of the near winners.)1

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.

Condorcet Quickly Picks Balanced Policies

  • No split-vote worries as duplicates don't help or hurt each other.
    The ad hoc majority ranks all of their favorites over other motions.
    Their top one wins.
  • Rank-choice ballots let us vote on related motions all at once.
    They simplify the rules of order and speed up voting.
    They reduce hidden votes and agenda effects from simple errors to killer and free-rider amendments.
  • Balanced policies avoid erratic or excessive changes.
    So they tend to be stable and decisive.
    They reduce the risk and fear in policy making.
    All this saves money and builds respect for leaders.
  • They don't favor a fringe group or the status quo.
    (But amending the current by-laws still can require a super majority.)

      (More merits of the Condorcet or “Pairwise” rule...)

Policies with Wide Appeal

 Open voting

Everyone helps choose our center.

A plurality or runoff winner gets no votes from the losing side and doesn't need to please those voters.  But a Condorcet winner needs support from all sides, because every voter can rank it versus close rival proposals.  Thus every voter is “obtainable” and valuable.  This leads to policy proposals with wide appeal.

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.

Chairs with Balanced Support

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.

Gerrymanders, rigged voting #1

Candidate M lost the last election by plurality rule.  Now let's say her party gerrymanders the borders of her election district.  They add neighbors (purple below) who tend to vote for her party; and exclude less favorable voters (the yellow voter missing on the left).  So now the new district is a “safe seat” for her party.

But M might lose to someone less moderate in her party's primary — the most challenging election she is likely to face.3

The party's activist wing often dominates the process of picking a nominee. This leads each party to elect reps with extreme positions — and they have no electoral incentive to compromise with other factions.

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

 Gerrymandered election

Now K has 3 votes. L has two. And M has four.


Bribes, rigged voting #2

Bribes, big campaign gifts, and jobs for friends can make some reps switch sides on a policy.  Condorcet rules resist corruption well, as bribing a few reps moves the council's middle, and the winning policy, only a little.

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.

Killer Amendments, rigged voting #3

Like a bribe, a “killer amendment” aims to make some reps change sides, to oppose a bill they had supported.  But Pairwise lets reps rank the original bill, no bill, and the “poison-pill” amended bill — so they are able to shun the pill.

Bob's Ballot
Rank        Option        
2Original Bill, the main motion
1Bill with Amendment One (a free-rider?)
7Bill with Amend. Two (a killer amend.?)
6Bill with Amendments One and Two
3Postpone for   1  days
4Refer the Bill to a Committee
5No Change in the status quo

Stacked Agendas, rigged voting #4

Meetings often make interlocking decisions one at a time.  They use a yes-or-no process, with or without explicit rules of order, agendas, and votes.  An early proposal may have to beat each one introduced later.  An early decision might shut out some later options.  So “stacking the agenda” is a way to favor some interests and hurt others.

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

Steering Analogy   

1890 Ransom E. Olds steamer car  

Mercedes-Benz Telligent Lane Assistent

Which is more stable and quick?


When choosing a voting rule, a new Mercedes costs little more than an old jalopy.  That price is a bargain when the votes steer important budgets or policies.

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.

How to Startup and Test Drive

It's easy for any group to test-drive a new rule in a survey.  Or a council can “form a committee of the whole”, to vote, tally and report results to enact by the old yes-or-no rule.

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.

 Tools Between People 

Voting rules affect our laws — and our views on life. By making us give either fair shares or winner take all,  rules shape how we treat each other and see our world. 

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.

Tools between people

Voting Helps Related Reforms

A news firm might inform us better if it is ruled, not by its owner and advertisers, but by its voting subscribers.  VoterMedia offers a low-cost method for all kinds of groups: vote using FS to pay prize money to the best local-news bloggers.  (McChesney and Nichols propose a $200 “news voucher” to help each voter fund their favorite ad-free news source.)

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.

Optical-scan ballots, post-election audits and open-source software check fraud by election workers and corporations.

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.

   Cost Effective Reforms ↓

Voting Reforms Are Cost Effective

These reforms open doors for popular changes.   e.g. Data shows Proportional Representation elects more women than plurality.  And this change leads to better health and education.

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.

Issue campaigns lobby reps every week for years. This eases one problem, but rarely fixes the source.

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.

   Costs compared to results from issue campaigns, elections or voting reforms

   Benefits Voters & Reps ↓

Review the Benefits for Voters and Reps    



Fair RepGive fair representation to all major groups.     So the council enacts laws with real majorities.

Center Elect a central chairperson with wide appeal. This swing vote pulls reps from many factions to moderate policies.

Center Reduce deadlocks and upheavals in budgets or policies.   Make shifts in power small, common and smooth.

Center Cut chances for agenda scams; detach poison-pill and   free-rider amendments. Speed-rank all options at once.

Projects Give all reps fair shares for optional projects and agencies.   And let the voters easily see each rep's spending.

    Why Take Votes  ↓



Why Take Votes

Groups 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.
A good tally can assure equality; even busy or unassertive people can cast a full vote.
Pondering a ballot or survey can motivate members to learn about setting the budgets and priorities.

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 Voting 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.

   Exit? ↓

Exit or Power

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.

   Conclusions ↓


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.
Thus they strengthen the mandates for winners.
That means they lift the proven support for:
Center  a Chairperson from a plurality to a majority of voters,
Fair Rep  a Council from a plurality to over three quarters,
Budgets  a Budget from a few power blocs to all members,
Center  a Policy from a one-sided to an over-all majority.

This page shows different voting uses
need different kinds of voting rules.
Politics is more principled and
governance more legitimate with
fair shares for seats and money, and
true majorities for executives and policies.

    Actions  ↓


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:
Organizing  Organize Voters,          with Transferable Votes.
Fair Rep  Represent Everyone,     with Proportional Representation.
Projects  Empower Everyone,      with Fair share Spending.
Center  Center Policies,            with Pairwise Winners.

This website has sim games and handouts,
plus free ballot-entry and tally software.

   Printouts ↓

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.


This 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:
elections and legislation, single winner and multi winner.

Search Accurate Democracy


Some people want a better Chinese translation. Chinese
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?