Different uses for voting need different types of voting.

Primer on voting systems

A Movable-Vote Workshop

Voting rules hide philosophies of government.
Get your hands on 4 great voting rules.
See fair-share tallies organize voters.
Vote fast on budgets, policies, and projects

This workshop shows the simple steps in each tally.
It is much more fun, and memorable, than a lecture.
Voters elect varied treats at the end. Eat the winners!


Instant Runoff Voting elects one candidate.
Single Transferable Vote elects several.
Movable Money Votes buy public goods.
Condorcet Pairwise Voting centers a policy.
Six voters placing their cards.


 A Tally Board Has:

  • A card for each voter,
  • A column for each option,
  • A finish line for the favorites.

Card E
Card D
Two single cards, stacked
in a candidate's column.

Instant Runoff Voting Elects One Candidate

For a tabletop tally by Instant Runoff Voting (IRV):
  • The finish line marks the height of half the cards plus one.
    That is how many votes a candidate needs to win.
  • If no one wins, eliminate the weakest candidate.
    Draw names from a hat to break ties.
  • If your favorite loses, move your Post-it, card or token. Give it to your next backup choice.
  • Repeat until one candidate reaches the finish line!

The chart below shows four columns on a tally board.
The voting rule eliminated Anna, as she was the weakest candidate
in first-rank votes; so JJ moved his card to his next choice.
Then Bianca lost; so the voters DD and GG moved their cards.

Tally board with 4 candidate columns

By organizing voters, Instant Runoff Voting ends:
Spoiler candidates and choices limited to the lesser-of-two-evils;
Costly runoffs and winners without majority mandates.

IRV elects leaders in London, Sidney, San Francisco and more.
It elects student leaders at Duke, Harvard, MIT, Stanford…

Questions on Instant Runoff Voting

1. A card that moves is no bigger than any other vote: True,  False, 
    Does its voter have more votes or power than any other voter: ?  
2. Your backup choice cannot hurt your first choice: True,  False, 
3. Only one candidate can reach a 50% + 1 vote finish line: True,  False, 
4. Who could use Instant Runoff Voting ? 
Answers:  Put your mouse pointer on a question, but do not click it.

Single Transferable Vote Elects Several Reps

For a three-seat election by Single Transferable Vote (STV):
  • The finish line marks the height of a quarter of the cards plus one.
  • Do not give a card to a candidate who has finished.
  • Eliminate the weakest candidates one at a time.
  • Move your cards until three candidates win!

Single Transferable Vote is used in some Australian and Irish elections, at Harvard, MIT, Oberlin, Princeton, UC Berkeley, UC Davis, and Vassar, at Oxford and Cambridge, in some unions, in the Church of England, and in voting for Hollywood’s Oscars.

It gives each group their fair share of voices on a council.
It often elects more women and minority candidates.
It increases choices for voters and turnout of voters.
It makes more “effective votes,” the number needed to elect the council.

Questions on Single Transferable Vote

1. Only three candidates can each win 25% plus one vote: True,  False, 
2. What total percent must the three STV reps win ? 
3. Your backup choice cannot hurt your first choice: True,  False, 
4. What is the threshold for winning one of five seats ? 
5. How can groups you know use the Single Transferable Vote ? 


Movable Money Votes Pick Public Goods

For Fair Share Voting by Movable Money Votes (MMV):
  • Let's say we each put in $1 to buy some items.
    You get two 25¢ voting cards and a tall 50¢ card.
  • We decide an item needs modest support from 8 of us
    to prove it is a public good worth public money.
    So the finish line marks the height of 8 single cards.
  • You may put only one of your cards in a column.
    So you can't dump all your cards on a private item.
    Tip: Give your tall 50¢ card to your favorite item.
    This way 4 eager voters can fund a low-cost item.
    So the voters’ number and zeal both count.

  • A costly item must fill several columns A column here
    holds $2,
    so a $4 item must fill two columns.
  • When an item wins, the treasurer hides its cards, and then
    excludes any item that costs more than all the cards left.
    Then one at a time, we reject the least popular item,
    with the lowest level of cards in its columns.
  • Move your cards from a loser to your next choice.
    (If allowed, consider briefly withholding your card(s) from a lower choice so it loses instead of a higher choice.)

    Voting stops when all the items still on the table are paid up.
    Only a few items can win, but all voters can win something!

Fair Shares Set Budgets

  • Each funding level is like another project:
    it needs enough cards to fill it up.
  • The “$4 carton of OJ” has two columns.
    The “$6 bottle of OJ” has just one more column.
    A supporter must help fill the lower level first.
  • One at a time, the weak levels lose and the money
    moves to help your highest ranks still in the running.
(Each funding level of an agency is treated as project.
But an agency starts with [80]% of its recent budgets.
So a member cannot give it zero and “steal a free ride.”)

Participatory Budgeting lets neighborhood assemblies spend
part of a city’s budget.  Porto Alegre did this first in 1989;
now it is used by hundreds of cities and towns in Latin America.
But most still end it with the old winner-take-all voting methods.

FSV is new!  Try it!  You will build a strong democracy.

Questions on Fair Share Voting

1. Should we let each member fund private items ? 
2. Should people who pay more taxes or dues get more
    power to spend public money  ?  

    to set public laws  ?  
3. Should a rep’s votes be so clear to voters ? 
4. Could your second choice hurt your first choice ? 
5. How can your groups use Movable Money Votes ? 

Pairwise Rule Centers a Policy

Here is a hands-on way to show the Marquis de Condorcet's
Pairwise rule:
  • Policy C's flag is at our center, by the median voter.
    Three flags surround C, about 5' from it. (1.5m)
  • Pairwise asks: “Are you closer to flag A than flag B?
    If so, please raise your hand.”  Then test A against C, etc.
    We put each total in the Pairwise table below.
  • The winner must top every rival, one-against-one.
against  A B C D
for A 2 2 3
for B 5 2 3
for C 5 5 4
for D 4 4 3

Who wins this contest ?  A B C D 

Pairwise is a Wide-Appeal Contest.

  • Flag C has a short Red ribbon and a long Blue one.
  • If the Red ribbon gets to you, the Red policy
    gets your vote with its narrow appeal.
  • But if the Red cannot touch you, the wider appeal
    of the Blue policy gets your vote.  Which one wins?

 If the poles are places for a heater in an icy cold room. 
A) Do we put it at our center or in the biggest group ? 
B) Do we turn on its fan to spread the heat wide ? 

Questions on Pairwise Voting

1. Can voters on the fringes affect the Pairwise result ? 
2. Can the median voter(s) enact any policy alone ? 
3. Does Pairwise favor balanced or one-sided policies ? 
4. Does it favor narrowly-centrist or broad policies ? 
5. Does it eliminate the weakest option and move its ballots ? 
6. Should a first-choice vote count more ? 

Full-Choice Ballots

Only small groups can use cards for voting.  Big groups use paper ballots.  They are often tallied by computer, with samples checked by hand. A ballot printed and checked by its voter, and later by a risk-limiting audit, can catch ballot box and tally frauds and errors.

Check mark ballots badly oversimplify most issues. Such falsely limited choices let voters see only two factions, “us versus them” or “left versus right”. This tends to polarize debates, harden opinions, increase conflicts.

Ranked choice ballots reduce those negative results. They let a voter rank his 1st choice, 2nd choice, 3rd etc. Ranks can reveal a great variety of opinions. Surveys find most voters prefer ranked choice ballots.

Fun votes include dinner-party music, favorite videos and snacks, group vacations, pizza toppings, Ben & Jerry’s, sports stars, actors...

Party Menu

Fill only one “O” on each line.
Best  - RANKS -Worst
Deserts 1st 2nd 3rd 4th 5th 6th
Fruits & Nut Platter
12 Chocolate Brownies
12 Choc. Chip Cookies    
4 Choc. Fudge FroYos
4 ‘’ Cheesecake Slices
6 Choc. Mousse Hearts

Which wins a plurality?   Hint: 5 chocolates vs. 1 nut.
And the first name on a ballot gets a 2% - 9% boost.

Other pages tell the merits of full-choice ballots and show examples of preference ballots.

For anonymity in tabletop voting, you may put your ballot in a box and pull out another voter’s, then move cards for that voter as someone else moves yours.


The best voting rules are fast, easy and fair.
They strengthen votes and thus mandates.  That means
they organize voters and lift the number supporting:
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,



This workshop is part of a free book for printers or tablets. The book has the primer, colorful graphics from both PoliticalSim™ and the budget voting game, and data to compare nations. A colorful copy is free for college libraries that will keep it in their catalogue and open-access shelves for six years. The supply is limited, so tell a librarian now!

 Contact Accurate Democracy  Contact Accurate Democracy  Contact Accurate Democracy

You may download voting cards formatted in Microsoft Word or Excel, free software, and a template for full-choice ballots.

It is rare to lecture on voting rules and find a student who doesn't get it.  But many forget the tally logic in a month, simply because they have not used it and don't expect to soon.  This workshop creates strong memories by involving a student's senses, physical movement, social interaction, and a favorite treat at the end.

Accurate Democracy is organized by uses of voting:
elections and legislation, single winner and multi winner.

The next section of the book has another colorful way of making elections visible. Here are the web pages with those graphics for Single Transferable Vote and Movable Money Votes.


Search Accurate Democracy


Workshop ballot