Different uses for voting
need different types of voting.
Voting systems and election rules for Accurate Democracy

Student's Guide to
Tabletop Tallies

Introduction to voting systems, chapter contents

Tabletop voting is a hands-on experience for students who like to learn by doing.  The games are simple, memorable introductions to great voting rules. 

Our purpose is to see a fair-share tally organizing voters into a multi-winner decision.  Concepts to learn include a transferable vote and a winning threshold.

We will see several rules that use transferable votes.  We start with the simple, one-winner rule which leads to multi-winner rules for electing a committee and selecting projects and then to funding agencies.

(Each rule has other web pages detailing its logic, uses and effects.  This introduction to transferable votes is available in several styles.

This introduction to transferable votes is available in several styles.  The booklets are easy to print on legal-size paper then cut across, stack and fold.  They fit in the Primer.  The single sheets print on letter-size paper.
Styles:AcrobatMS WordOther
Dot Lists
BookletIRV, STV…BookletSlide show
One sheetIRV, STV…HandoutWeb page
One sheetIRV, STV…Class This page

You may download a large-font edition in Acrobat IRV STV Big.pdf, or MS Word IRV STV Big.doc.

You also may download a full-choice ballot, free software, and voting cards formatted in Microsoft Word 2000 or Excel.)

The Tally Board      ”Six

This "vote transfer board" has a column for each candidate. Each voter gets a "card" to cast in the column of his favorite candidate.  A candidate wins if her column of cards reaches a finish line.  ("Her" refers to candidates; "he" refers to voters.)

Our V-shaped paper cards fit over the columns of an paper panel folded accordion style. It is big enough to let ten voters at a time place their initial votes.

Your card has a colorful ID label so you can find it easily and move it yourself.  This will help you get a feel for transfers.  But a voter must not move another voter's card.

Card D    Card E
Two Single Cards.

Electing One Winner by IRV

For Instant Runoff Voting (IRV) the board's finish line marks the height of half the cards plus one.  The winner is the candidate whose cards reach this quota or "winning threshold". 

If no candidate wins half the cards plus one, the candidate with the fewest is eliminated.  (A dice or coin toss can break ties.).0 A voter who supported that candidate now has to move his card to his next choice: he "transfers" his vote.  Cards are counted again and this step is repeated until...  The candidate whose cards reach the finish line wins!

IRV is used to elect the President of the Republic of Ireland, the Mayor of London and the Australian lower house. It is used to elect student officers at over 20 top American universities including Carlton, Cal Tech, Duke, Harvard, Johns Hopkins, MIT, Rice, Reed, Stanford, UC Berkeley, UC Davis, UCLA, Vassar, William & Mary, and the Universities of Illinois, Maryland, Washington, and Wisconsin.

By organizing voters, IRV avoids "spoiler" candidates and the lesser-of-two-evils choice, costly runoffs and winners-without-mandates.

IRV Questions

1. Can two candidates reach the 50% +1 finish line?
2. Can your second-choice vote hurt your first choice?
3. Is a transferred vote bigger than any other vote? Does its vo¬ter have more votes than any other voter, or more power?
  What do you think is more fair, to throw out ballots or move them to each voter's next choice? Would you want your ballot to help your next choice or to be thrown out?
4. How could your group use Instant Runoff Voting?

A sample ballot is pictured below.  Its issues include dinner-party music, favorite videos and snack foods.  Optional topics include, group vacations, pizza toppings and ice creams.

Those who want anonymity may put their ballots in a ballot box and pull out someone else’s or a "mail-in" ballot.  The mail-in ballots make our electorate more diverse.

Electing a Council by STV

For a three-seat election by Single Transferable Vote (STV) the finish line marks the height of one quarter of the cards plus one.  (Droop quota)  To win a seat, a candidate's cards must reach this line.

A voter may not give a card to a candidate who has crossed the finish line.  (So there are no "excess votes" to transfer.)

The weakest candidates are eliminated one at a time and students move their votes until three candidates win!

STV is used in Australian and Irish elections, in the Church of England, and at universities including Oxford, Cambridge, Berkeley, Harvard, Princeton, Vassar and Whitman.  It increases choices for voters turnout of voters, elects more women and gives each group their fair share of representatives.

STV Questions

1. Can four candidates reach the 25% +1 threshold?
2. What is the threshold for winning one of five seats?
3. Can your second choice hurt your first choice?
4. How could you use the Single Transferable Vote?

Funding Projects by MMV

Movable Money Votes (MMV) give a costly item several columns to fill.  If each column represents $100, a project that costs $200 needs to fill 2 columns.

The bylaws might say an item needs moderate support from at least 8 voters to prove it has broad public support for public funding.  Columns are therefore 8 cards tall.

And because every 8 cards will fill a $100 column, we hand out 8 cards for every $100 in the fund.  Those cards can fill just enough columns to use up the fund.

Each voter receives a set of cards to represent his share of the funds.  You may place only one card in a column.  This prevents you from dumping all your cards in one column, so it keeps the threshold for public money at 8 moderate backers.

You might receive two single cards and one double card to represent your [$50] share of the money for projects.  The usual strategy is to put the double card vertically in your favorite column to raise it quickly.  This way, 4 enthusiastic supporters can fund one low-cost item.

When an item wins, the banker removes or hides its cards.

We eliminate unpopular items one at a time.  First we drop items that cost more than all visible cards.  If there are no such costly items, we drop the one with the smallest fraction of its columns filled.

When a favorite is threatened, you may try to save it by briefly re¬moving your cards from lower-choice items.

If 1 of yours looses, move your card(s) from it to your next choice.

Voting ends when all remaining projects are paid up.  (Any leftover cards would go to an emergency fund, an endowment or other politically neutral uses.)

Only a few items can win, but all voters can win something!

MMV Questions

1. Can your second choice hurt your first choice?
2. Should we drop the item that has 1) the lowest percentage of its columns filled, or 2) the greatest number of empty spaces?
3. When paying for public goods, should a person's taxes equal his or her benefits? Should people who pay more taxes get more power to spend public money? to set public laws?
4. Do you belong to an organization that could use Movable Money Votes? MMV is new, try it! Such accurate democracy will help your group directly and set an example for others.

The introduction to voting on projects describes some merits of Fair-share Spending by MMV.

Adjusting Agency Budgets with BRV

Budget Refill Voting (BRV) has several columns for a costly department to fill, as MMV did for a costly project.  But an agency cannot be eliminated during BRV. A supporter’s cards raise its budget. 

Each column of an agency begins the tally from a starting line $100... below a goal line — which may be last year's budget or one set by a Median Voter Process.  Voters may push an agency above its goal line, but its gain will be another's loss.

Say 20 voters want to budget 4 small agencies with 1 column each plus 3 with 2 columns each. They decide each agency needs moderate support from 10 vo¬ters to restore its previous funding. So a column needs 10 single cards from 10 voters to reach its goal line –- or 5 double cards from enthusiastic voters can maintain fund¬ing for a small agency.

In this example, each voter gets 5 cards.
(That’s because 10 columns * 10 cards each = 100 cards needed to refill all columns.
And 100 cards / 20 voters = 5 cards for each voter.)
You may get one double and three single cards.

As a voter, you should set a target budget for each agency and rank your priorities.  As a budget nears your target, its priority likely goes down, and at some point you’ll want to move your cards from it to your next under-funded priority.  Reacting to other voters is key!  (This makes us use cards designed slide down a column to fill in when someone removes cards below.)

Voting stops when a hidden timer sounds and voters lose cards that are not on the board.  This deters people from faking votes until a last moment switch.  A two-thirds majority may reopen voting.

BRV Questions

1. Does each voter have transferable votes?
2. Do agencies have winning thresholds?
3. Can your second choice hurt your first choice?
4. Where could you use Budget Refill Voting?  It's new, try it!

The cards and columns can be on spreadsheets.  On-line "cards" are easier to move than real cards and any number of voters fit at the "board". Tally software also make the STV or MMV transfers easy and quick.  A voter just ranks the options once and the computer does the rest.

Conclusion      ”Six

Transferable votes quickly organize powerful groups support¬ing popular choices.  They are a great improvement over primitive rules when selecting a person, a whole committee, a set of projects or renewed budgets.

Politics is more principled with fair shares for seats and money, full majorities for executives and policies.

Fun ballot issues include dinner-party music, favorite videos and snack foods, group vacations, pizza toppings, Ben & Jerry’s, sports stars...

Those who want anonymity may put their ballot in a ballot box and pull out another student’s or a “mailed-in” ballot.

These are usually the best rules for distributing winners to interest groups.  But this hints that they often are not the best rules for picking the one central policy with the broadest support from all groups.  That goal will be the topic of the next chapter on Pairwise Tournament Tallies..

Teacher's guide

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