Voting Rules for

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.
The results 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 Spending: Old Problems, Principle, MeritsNew
Pairwise CenteringPolicy Decision Condorcet & Rules of Order: Principle, Merits, Patterns.
    Philosophy.   Conclusions.   Prints.   español.    ↓ Next Slide ↓ 
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 screens, or printers and 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 North Carolina, there were 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.

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.

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?

Our defective voting rules come from the failure to see there are different uses for voting; and these require different types of voting.
Voters waiting waiting, by Kiichiro Sato

Will their votes have any effect?

We all know how to decide the simplest sort of issue: A question with only two answers must be answered yes or no. For such an issue, the “yes” and “no” votes are enough.

But as soon as three candidates run for one office, the situation becomes more complicated. Then a yes-no vote is no longer suitable.

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.

Such a council (or budget) receives far more than half the votes!

      Eras ↓

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.  So the winners get only a weak mandate from the voters.

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.

Each district's bias tends to make its only seat 'safe' for one party. So most voters get no real choice. A few of those who do get choices can make majorities swerve from side to side.

A council majority sets policies (dark blue in picture) in a war of winner take all.

 Plurality election
$  $  $  LAWS   $  $  $

Typical Council Elected By Plurality Rule

   1900s ↓

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 voting district.  It gives a group that earns, say 20% of the votes, 20% of the coulcil seats.  Thus PR delivers fair shares of representation.

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, which then enacts policies skewed to one side.

 Proportional Representation
$     $  $  LAWS  $  $      $

Typical Council Elected By Proportional Representation

   2000s ↓

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 PR 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 unite the best ideas from all groups.

 Mixed Member Proportional MMP

Ensemble Elected By Central And Proportional Rules

   Progress ↓

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.

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.

   Example ↓

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.”
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 anyone win a majority?   Yes, No.
Who wins the plurality or largest share?   K, L, M.
Who wins the second largest?   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 ↓

Runoff Election

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

Two voters who supported 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 the voters?”)

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

 Runoff election

Candidate M wins the runoff.

   Two Dimensions ↓

Politics in Two Issue Dimensions

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

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 ↓

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.

   IRV_2 ↓

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 (2nd) 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.

   IRV_3 ↓

Some Benefits of Instant Runoff Voting are:

  • A majority winner from one election, so no winners-without-mandates and no costly runoff elections.
  • Higher voter turnout, it often drops in runoffs.
  • Less campaign spending, it often goes up in runoffs.
  • Less divisive campaigns and attack ads, as a candidate tells rival factions why she is their best backup choice.
  • No hurting your first choice by ranking a backup, as 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 parties, as votes for minor candidates move to each voter's more popular backup choices.
   IRV_4 ↓

Plurality Voting Patterns

In South Korea's 1987 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.

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 some split elections and their tragic results?)

   IRV_5 ↓

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 ↓

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.”

B wins 5 votes as J gets 4 in the top group.

A minority with 11 voters elects a majority, 2 reps. But if evenly spread out, they would elect 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 get one.

   Full Rep_2 ↓

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.
   Full Rep_3 ↓

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.
  • Women get elected about three times more often. so
    Majority rule improves — also by few wasted votes, real choices, turnout and reps with equal support. so
    Policies match public opinion better.
   Full Rep_4 ↓

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.

(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-Winner Districts to a layer of SWD 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.  Voters also elected 3 Polynesian reps and 1 Asian rep.

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

   Why Elect Women ↓

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-winner districts. Their districts elect few women; but in the same elec┬Čtion, 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. 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. In one-seat districts, new parties split a side and lead to certain defeat. But PR promptly gives seats to a new party, if a big group of voters support it.

This credible threat made some parties decide that job experience was not as important as gender balance. They dropped some experienced men to make more room for women on the party list. And they won. Now they are incumbents with experience, power and allies.

   Rules and Results ↓

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.

In a SMD, a landslide winner wastes surplus votes. But Fair Rep elects reps with equal numbers of votes. So any council majority 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.

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.

The countries with the best voting rules get the best quality of life, as measured in their international scores. So the people who want to raise the quality of their city or country all need to take action for better voting.

   Related reforms ↓

Related Election 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 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.

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.  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.

Initiative voters get more choices and power through ranked-choice ballots and better 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.

    Spending ↓

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 might be the only votes in a direct democracy.

Proportional Representation distributes the council seats fairly.

In the same way, Fair-share Spending allocates money fairly.  It is the next logical step.

Democratic rights fulfilled through history:
Full Rep Voting for rich men, poor men, “colored” men, women.
Full Rep Proportional Representation for large political minorities.
Projects Fair-share spending by big groups of voters or reps.

 Fair shares mean minority voters also have some power.


Fair shares give minority voters some power.

   Spending_2 ↓

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.

Bad election rules are even worse at setting budgets: They're not 'cost aware,' and so increase tactical nominations and voting.  A majority needs many candidates to elect several; but if votes split badly, they win less than their share.

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

   Spending_3 ↓

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.

   Spending_4 ↓

Local Control of Central Funds    

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

Earmarks let powerful reps take much more money to their districts than most reps do.  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 wasting 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.

Participatory Budgeting is a big step up for democracy. It lets local meetings research, talk and vote on how to spend part of a city's budget.  In South America, it spread from 1 city in 1990 to over 1000 today.  The World Bank reports that the Participatory Budgeting or PB process tends to raise a city's health and education while reducing corruption.

For the last four years, a savvy alderman in Chicago gave his “discretionary fund” to the PB process.  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.

Even the winning votes were wildly unequal.  A vote for the play­ground was worth $501.  But a 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 reform is hard because unfair rules have become entrenched by centuries of use.  Because PB is still young, we have a rare opportunity to introduce better voting rules now — voting rules that are more expressive and more fair.

   Spending_5 ↓

The principle of Fair-share Spending 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 needs grants from many voters to show that it is a common good worthy of group funding. 
So we let a voter fund only a fraction of a project.

How does it work?  Like IRV: You rank your choices.

Then your money moves to help 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 movable-vote game makes this process easy to grasp.)

   Spending_6 ↓

Merits of Fair-share Spending

For Picking New Projects

  • Your share helps buy your choices. This motivates voters to turnout and vote for cost-effective projects. So a fair, cost-aware tally buys the most joy per dollar.
  • A small project uses only a small part of your share, so you can afford to support more projects. Thus FS is fair to a project of any price and to its supporters.
  • 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.
  • Your votes move from losers to backup choices, so
    Less worry that similar projects will split the voters
    More voters and legitimacy for the set of winners
  • 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.
  • 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.

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 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 taxes and bureaucracy. And it funds big groups even if they're scattered.
   Spending_7 ↓

Fair share Spending in Participatory Budgeting       

  • Fair-Share Spending 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 Spending 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 30 years.  In 2007 they first used this new method of Fair-share Spending by Robert Tupelo-Schneck PhD.
   Spending_8 ↓

Fair-share Spending 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 out 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.

   Spending_9 ↓

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.1 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 share the cost, each of them pays less.

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 vote. 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.

One Voter's Ballot: A group of 100 set their base number at 25 votes. 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 was so popular, I paid only 2% of it. Did I waste much power by voting for this sure winner? How many ballots shared this cost?

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”. (A second poll could let voters try to restore and increase funding to their favorite items.)

   Spending_10 ↓

The Principle in Budget Refill Voting was:
Majority rule,
within a balance of forces.

So if we all agree, we can change budgets radically.
But if many disagree, they can moderate the changes.
Yet a minority cannot slow the budget process.

Each agency starts with [80]% 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.

A minority can moderate a budget's change.
But a majority can make it rise or fall.

* To vote less than about [80]% 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.

   Policy ↓


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.

   Policy_2 ↓

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 the “Condorcet 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 Pairwise picks a central chairperson or policy.
Is it likely to elect diverse reps?     Yes,  No.

 Condorcet contest 3

L is nearest 6 voters;     M is nearest 3.

   Policy_3 ↓

The goal of the Pairwise 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 no one does, IRV can pick one of the near winners.)

If another rule picks a different winner our “round-robin tournament,” or Condorcet winner ranks higher on most ballots.  So it wins a one-against-one majority over that other rule's winner.

   Policy_4 ↓

Pairwise Tallies Quickly Pick Balanced Policies

  • Rank-choice ballots let us vote on related motions all at once.
    They simplify the rules of order and speed up voting.
    They reduce agenda effects such as simple errors, poison-pill
    or free-rider amendments.
  • Balanced policies avoid erratic or excessive changes.
    So they tend to be stable and decisive.
    That saves money and builds respect for government.
    They reduce the game-of-chance and fear in politics.
    They also cut the payoffs to big campaign sponsors.
  • They don't favor a fringe group or status quo (unless required to i.e. by-laws).
  • Pairwise can elect a fairly neutral judge or administrator.
    It can elect a central, often neutral, moderator for a council
    — particulary for a centrally-balanced “ensemble council.

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

   Policy_5 ↓

A Popular and Balanced Policy

 Open voting

Everyone helps choose our center.

A policy needs good marks from voters on all sides.  That is because every voter can rank it compared to other policies.  So all voters are “obtainable” and valuable.  This leads to policies with wide appeal.  (A plurality or runoff winner gets no help from the losing side and need not please those voters.)

The Pairwise winner is central and popular:  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.

This is an attractive service for consultants to offer clubs, co-ops, colleges and companies.  It might become a popular reform.  Even reps, who tend to oppose changing the election rules that gave them power, may favor legislative rules that reduce polarization and deadlock.

   Policy_6 ↓

A Moderator with Balanced Support

Most progressive voters rank Kennedy [Livingstone, Lafontaine] above Clinton [Blair, Schröder].  So to win a majority over Kennedy, Clinton must outrank him on ballots from centrists and conservatives.  She cannot hope to be the first choice for conservative voters; still, she must seek their favor.

Conservative voters rank Bush [Major, Kohl] higher than Clinton.  So to win a majority over Bush, Clinton must appeal to centrists and progressives.

Every candidate needs the centrist voters, of course.  But every candidate needs the progressives and conservatives too.  When compared with Kennedy, Clinton needs those conservative voters.  And when compared with Bush, Clinton needs the progressives.

In this Pairwise election of a moderator, a less controversial candidate might top each of these polarizing politicians. To pick a moderate, an election district needs diverse voters.

(A later page shows an interactive Pairwise tally table.)

     Rigged_Votes_1 ↓

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 she may lose a party primary to someone less moderate.
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.

 Gerrymandered election

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

     Rigged_Votes_2 ↓

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.

Poison Pills, rigged voting #3

Like a bribe, a “poison-pill 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.

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.  The first proposal may have to beat each one introduced later.  The first decision may shut out later options.  So “stacking the agenda” is an easy way to favor some interests and hurt others.

Or people may talk about all options at once but never clearly tell (vote) their second and third choices.  So a few people pushing a single idea can appear to be the strongest group.  And one person with a balanced solution but no eager supporters might drop it.

A yes-no process may let a committee report only two options for all members to choose between.

The best rules avoid all those problems by ranking the competing options on one ballot.

   Tools Between People ↓


Democracy         Tools Between People        Democracy

Voting rules affect our laws — and our views on life. By making us give fair shares or winner take all,  voting shapes a way we treat each other and see our way of life. 

Official rules model the goals for shared decisions. So those rules can affect the patterns used by workers, friends and neighbors.

These rules help make it safe and easy to cooperate. This favors people who tend to do it and leads others to do it more often.

The best tools help groups embrace diversity and freedom. So the group's size and resilience may increase.

Tools between people
Happiness is strongly linked to good relationships.  So a good way to raise happiness is to improve the tools between people.

   Why Vote ↓

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 more, because it won't favor a fringe opinion.  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.

   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 ↓

Benefits and Costs


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,
Full 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.

    Benefits  ↓

Review the Benefits for Voters and Reps    



Full 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 moderates reps from interest groups.

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 equal funds for projects and agencies.      And let the voters easily see each rep's spending.

    Reform!  ↓

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

   Steering Analogy ↓

Steering Analogy   

1890 Ransom E. Olds steamer car  

Mercedes-Benz Telligent Lane Assistent

Which is more stable and quick?

Help your college, co-op, club or congregation.  

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.

    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.
Full 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, a 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?