Fair-Share Ballots

Often a few people in a large group think bigger is better, so they give high numbers to their favorites.  These voters and others are more likely to get what they want with ballots that grade the items.

Voters can type in their own grades at a personal-computer voting booth -- but those are expensive so voters often have to wait in line because there are not enough booths.  Voters more often write grades on paper ballots which clerks then enter and double check for a computer tally.

Voters can pencil in dots on a "bubble-form" paper which is read by an optical scanner.  The ballot shown here lets a voter grade items from A++ to F- -.  That allows 30 different grades; so a voter can use up to 30 levels of preference on the ballot.

Basics of Movable Money Votes

This demonstration follows an introduction to Single Transferable Vote, which may include an STV workshop with tabletop voting. Parenthetical comments are for math-savvy readers. Comments in brackets are for teachers.

What are some aims in voting for projects?
[As audience answers, look for these points and more.]
• Pick $100... worth of projects.
• Give each voter a fair share of spending power.
• Prove breadth of support for each project.
• Prove intensity of support for each.
• Set the budget for each.
• Spread the cost of each project among its supporters.

Let's say the quota is ten; that means to win public funds, an item must have strong support from at least ten council members.  So one rep may contribute only one-tenth of a project's budget.

I'm giving my first choice a tenth of the money it needs.  If nine other people give similar offers, it will have all the money it needs.  [Spread a line of money on the table, 1 by 2]

1st Choice

One-tenth of a low-cost project will be less than one rep's share.
[Wave the rest of my paper money.]
In fact, the entire cost of some projects might be less than one share.

Now, I could just hold on to the remainder of my share, as I watch each of my lower choices fall into last place and get dropped.  Or I could offer some of my money to my second and third choices.  It makes sense to help them avoid elimination.

[Continue the line of money on the table with two short lines, side by side,  1 by 4 and 1 by 2.]

1st 2nd 3rd

But how much should I help lower choices?  I don't want my vote for a lower choice to prevent its elimination, if that means my first will be eliminated.  So I have the option that my lower choices will not count if my first choice is the weakest candidate.  Likewise, if my second is threatened with elimination, my votes below that temporally do not count.  So helping a lower choice never threatens a higher choice.

[Hide the third item's money under a piece of paper.]

( The option to protect favorites has a down side:  While hiding lower-choice votes, I'm helping fewer items.  So I might see some of my lower choices eliminated and then see my favorite eliminated anyway.)

OK.
[Uncover item three.]

If my second choice is eliminated, [Remove its money.] others move up, [Slide column three next to column one.] then my ballot transfers that money to my next choice.  [Spread the money in a new third column.]

That's a transferable-vote rule for projects.  Any questions up to this point?

We can make a tally even better at funding favorite projects.

I've spread three columns of money up to this one- vote line.       [1 by 2, 1 by 2, and 1 by 4, topped by a ruler.]

1st 2nd 3rd

The more expensive the project, the wider its column.  Here's a low-cost project with a narrow budget, and to the right a costly project with a wide budget.  My offers to my favorite projects use up all of my share of money.

I would like to give my first choice more than one vote.  That will help it win.

To give a project two votes, I must give it two donations.  So I need to double its column height up to this two-vote line.  But where can I get that money? . . .  Sure, I take it from my lowest choice.  And now it has less than one vote. [Turn its money sideways.]

1st 2nd 3rd

The tradeoff is that lower choices get less than one vote.  Is it obvious that this will help fund first-choice items?  Does it seem fair to move money so the first choice gets two votes and a lower choice get only a half vote? . . .

( This is also a way to protect favorites.  It is a compromise between leaving my favorite vulnerable to my votes for lower choices, versus leaving lower choices with no votes.)

Of course, to make the quota work, the rules limit the number of votes I may give any one project.  A good limit is two votes.

Now the height of the first column changed and the height of the others changed.  What quantity is constant on this table? . . .  Right, the money!  One share, that is the area covered by my money.  The width of an item's column(s) is also constant; the width is one-tenth of the budget the item should get.

( Note that the total width also equals one share, forcing me to spread out my money.  If I could concentrate my influence by giving the maximum vote to as many items as I could afford, it would, in effect, reduce the quota.  Again I would not be helping my first any more than my third -- so the tally might end up funding the third choices instead of the first choices.)

How Does My Ballot Allot My Share?

Easy Ballot Calculations

The workshop introducing transferable votes gives the easiest example: Each project gets one column for every $100... in its price.  Each voter gets a bag of cards, tokens for his share of the funds.  The bag holds small, medium and large cards.  He puts his largest card in the first column of his favorite project, and he may give more than one card to an expensive project with more than one column.  A project wins if voters fill all its columns.

A picture of cards, lined up by size, graphs the funding "utility" curve inherent in each bag of cards. These 6 cards are made of 12 alphabet blocks and the average card, with 2 blocks in this case, counts as 1 vote.

The easiest computer tally is analogous to the workshop's tally board for Movable Money Votes.  A computer program lets a ballot place dozens of cards, each slightly different in value.  It puts the biggest card in the first column of the voter's favorite item.  Then the second-biggest card goes in the item's next column, if it has more than one, etc.  When the ballot has put one of its cards into each column of the favorite item, it offers the next, slightly- smaller card, to the first column of the voter's next- favorite project.

When a voter grades several items as tied for his next card, which of them gets it?  The card goes to the item with the lowest ratio of
Cards already given to the item  /  Item's number of columns.

A ranked-preference ballot lets voters decide which projects win funding.  But by itself, it does not let them say how much funding each project needs.  That may be best because many voters like to have each project's price set before they vote for it, so they know how big a project they are voting to fund.

A project's budget could be set by those who propose it, or by a cost-estimating committee, or by a general vote that selects the median amount voted for each proposal, or by all three steps taken in that order.  Perhaps that general vote should ask each voter to rank the item as he suggests its budget.  Then we could pick the median amount from votes of supporters, without voters who oppose the item.

( The MMV advanced ballot on a later page is more complicated partly because it lets only supporters adjust a project's budget, on the same ballot where they set its priority.

MMV advanced was invented first, using logic from Meek's and Tideman's advanced rules for making Single Transferable Vote even more fair.  MMV basic came out of practical considerations and experience.  It is much easier to explain and to program.  It is almost as fair to different groups of voters and efficient at funding winners favored by many voters. )

The next page adds more detail about the tally steps and how a ballot apportions money, labor or other resources among a voter's top-rated items.