Tally Rules for
Movable Money Votes

Movable Money Votes Using Cards

This form of MMV grows from the Single Transferable Vote tally analogy, and the Movable-Vote Workshop.

A discussion follows this list of the tally's features:

Proposals and Candidates
A) The bylaws may deter frivolous proposals by requiring a number of sponsors for each project.
A$) Each item's sponsor names its proposed budget.  A cost-estimating committee can give it a recommended budget.  Voters might set it by the median budget on supporters' ballots.  All three steps may be used in that order.

An approximate cost of each project must be set before voters can grade the proposals on cost effectiveness.

A general vote can select the median amount voted for each proposal.  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 tally calculation for advanced Movable Money Votes is more complicated partly because it lets only supporters adjust a project's budget as they give it a winning number of votes.)

Ballot
B) MMV lets each voter rank the candidate items, as in STV.
B$) A previous ballot may find the median budgets.

Quota
C) STV requires a candidate to win support from a large number of voters, a quota.  So does MMV.  An item desired by only a few people may be a good thing but it is not a public good eligible for community funds.  It may be funded with private money.

MMV quotas actually combine 2 quotas: a minimum number of supporters and the item's cost.  The item must fill both quotas.  The cost quota must be filled to prove the intensity of support.  The quota of ballots must be filled to prove the item's breadth of support.

Let's say the bylaws set a quota of ten.
Ten cards are needed to fill a column.
An item wins if supporters fill all its columns.
A winning item collects the offers from its supporters.
It's budget is the amount collected.
The supporters have funded it and used up some money.

As in Proportional Representation, the quota should be less than a majority.  The quota of votes is set in the council's by-laws.

(An organization whose charter, constitution, or by-laws require majority support for allocations can use MMV in a survey, or by turning into a "committee of the whole" to vote, tally and report its result for adoption by the usual rules.)

C$) MMV also requires an item to win its budget in contributions.  This proves the supporters think it is worth its cost.

Weight
D) STV and MMV give each ballot a fair share of power or weight.  A ballot's weight is used up as it helps elect candidates or fund projects.  In MMV a ballot's weight is money in an individual account.  This is usually an equal share of the FS fund divided among the number of ballots.
Weight = FS Fund / Voters

Under STV a voter usually helps elect just one rep.  Under MMV a low-cost item might cost its supporters only a little of their weights.  So a voter can help fund several items.

Eliminations and Transfers
E) Both STV and MMV eliminate, one at a time, the weakest item that fails to win quota.  Weight transfers to each voter's next favorite.  This avoids “wasted votes” for losing items, votes which if not transferred keep a voter from achieving his share of power.

Discussion

Using the median vote to set budgets limits the influence of exaggerating preferred budgets.  Exaggeration does not help raise the item's final budget.

Twenty years experience at one organization shows the largest group of voters stick with the recommended budgets.

Equity Process In MMV: Ballot Weights

Each voter may start with an equal share of the budget or shares may vary based on contributions to the organization.

( MMV takes its total budget as an external given.  It was developed for an organization that puts some of the coming year's projected surplus into a discretionary fund.  Asked whether we should let voters add personal money to their voting weight, thus increasing the budget, their personal “tax” and their influence on the public goods selected, they laughed, “No one would do that; we all want our personal funds for personal uses.”  Still, civic clubs and religious groups might choose voluntary donations. )

Utility Process In MMV: Variable Votes

Simplest Tally Logic

This logic is based on the tally board used in the workshop on transferable votes.

Let's say each voter's ballot gets 99 cards that range in size from 198 down to 2.  These numbers could be pennies, yen, euros, labor hours, gallons, liters, or another limiting resource.

The outer most loop, let's call it Drop1Loop, drops the weakest item and calls the CardLoop, unless all remaining items are fully funded.

CardLoop will loop once for each card, 99 times in this example.  It selects the card that each ballot will offer on this loop, starting with the biggest card on the first loop.  Then CardLoop calls BallotLoop.

BallotLoop calls each ballot once.  A ballot offers the selected card to the next column in the ballot's list of favorites.

A ballot remembers how many cards (not dollars) it has given to each item.  A ballot also can see how many columns an item has and limits itself to giving the item that number of cards, one per turn.  If the item is fully funded, the ballot gives the card to the voter's next choice.

A low-cost item is not eligible to receive cards if the current card is worth more than double the item's Cost / Quota.  That is two votes.  This keeps the quota real to prevent a small group of voters from funding a private item.  The inexpensive item's single column can fill up quickly as soon as smaller cards come into play.

Identical ballots have almost equal chances for offering cards to a favorite.  The first ballot called by BallotLoop might give one more card to an item than the last ballot called, if other ballots fill all the item's columns during that BallotLoop.  This difference is not important if each ballot has many cards.

By adding one small card at a time and stopping at the finish line, there are never significant “excess votes” to transfer.  By starting over after dropping each loser, voters can't hide cards by ranking a sure loser first.  Voters who sincerely rank losers high also pay their fair shares for their favorite winners.  So we have less need for Brian Meek's method to readjust transfers of votes from winner.

This tally logic uses whole numbers and could be done physically with real cards -- if voters were willing to spend many hours taking turns to each place one card at a time until all cards were used, drop the weakest, remove all cards from the board, and repeat taking turns to place one card at a time.

This physical analogy helps voters visualize the logic and welcome a computer's help with the tally.  A simulation of fair-share spending is free to download.  It shows 25 voter groups and 16 project proposals on a map.

[The results for the community would be much better than winner take all.  But the results for an individual would sometimes look illogical.

Say you prefer A > B > C > D... then A, B, and C each win.  Your personal result might show that your ballot contributes to A and C but nothing to B.  It can happen this way:  While you give big cards to A, other voters give big cards to B.  They pay B's full cost before A is paid up -- before your ballot would have started to give its smaller cards to B.

The same pattern occurs in STV elections but is less noticeable.  In a very simple case, you prefer A1 > A2 > B > C > D.  B wins.  A1 is eliminated.  Then A2 wins with many extra votes.  Your share of the extra helps elect C.

Meek's STV solves that.  But it needs modifications to get good cost/benefits in fair-share spending.  It is used in MMVa.]

Improving a Set of Winners

It is also important to find popular items eliminated early.  Such an item has broad but not intense appeal.  It lacks top ranks on a quota of ballots, so it is eliminated before the good ranks it earned on many ballots would give it funding.  Here are several ways to find and fund such items.

Loring Allocation Rules use a Pairwise Condorcet tally to fund a few broadly-popular, central winners before starting an MMV tally.  A voter does not spend any cards by giving a high rank to a Condorcet winner.  This Condorcet tally also reduces the “free riding” incentive for a voter to rank his sure-winner favorite low to avoid helping pay for it in the MMV tally.

The relatively simple “card” tally above may use techniques proposed to optimize sets of winners from Single Transferable Vote.  The most common process is reinstating one loser at a time to test its popularity compared to each and every winner -- which Nicholas Tideman suggests is a shortcut to approximate his Comparison of Pairs of Outcomes by Single Transferable Vote (CPO-STV).   I.D. Hill and Simon Gazeley have published a refined method for reinstating one at a time as “Sequential STV - a further modification.”  And James Green-Armytage has also contributed in “Computational Conservation in CPO-STV.”

Unlke candidates, projects vary greatly in cost to the voters.  So one-for-one substitutions do not work well.  A handful of people have suggested other ways to approximate CPO-STV.  But none of them considered selecting items needing different voting weights from supporters.

Sticky Items

Delete Last Loser

We want to give other items a better chance to use money offered to sticky items.  Release the offers for the last loser by pre-eliminating it.  Tally again.  This may be repeated for several rounds, increasing the number of items pre-eliminated.

Deleting the last loser can help an “exhausted” ballot which has money but no more favorites in the running, to distribute more of its money by giving more to each of its 'tally A' winners, and perhaps by helping new winners.  By giving more, the ballot helps other voters who support those winners, saving them money for their lower preferences.  These other voters likely have similar goals.

When a last loser is eliminated or suspended, its money is available, at long last, for offers to items ranked below it on a ballot.  Pre-eliminate the last losers one at a time to remove sticky items.  Deleting last losers one at a time and running the entire elimination tally many times obviously takes time.  But it is not expensive.

Both delete last losers and reinstating one at a time are powerful tools for fair-share spending.  The resulting sets of winner will be usually be very similar.  Experience will teach us which method is more fair to interest groups or better at funding favorites.  All forms of MMV are much more fair and efficient than old, winner-take-all rules.

The rules should specify what to do with any leftover money.  It can be put in investment, endowment, or emergency funds, given to all voters in the next allocation, or to other politically neutral uses.

We might improve MMV by giving each voter more cards, the same total value but with a smaller average value.  The “utility curve” inherent in the set of cards becomes smoother.  Math savvy readers will see this is a step toward calculus.

The next page shows how a ballot can use calculus to give voters a range of perfectly smooth curves.  But the benefits are probably small and the complications large for those who must program or explain that ballot and tally. 

The basic MMV on this page may be good enough for many groups.  In setting budgets as in electing reps, the difference between winner-take-all rules and fair-share rules is far greater than the differences among the fair-share rules.

p_options.htm explained other ways MMV can keep the order of winners and eliminations from making a popular item lose, and how voters may avoid buying two of a kind in rival proposals.  

fundRank.htm presents tables and charts showing variations on utility curves.

z_future.htm sketches ideas for other funding rules.

All types of voting can be improved and that is most evident in funding rules.  This page has explained the logic and arithmetic of basic Movable Money Votes.  Later pages explore the Loring Allocation Rule and optional features for MMV.

Sorry to say, some pages still show the creative disorder that often occurs during research and development.  (Humor: The latter pages show the creative disorder that occurs during evolutionary divergence when species proliferate.)

NEW   Free software in p_tools.htm gives a feel for grading, quotas, and varied budgets.  Download and play with the simple simulation game.  Microsoft Excel 5 or higher is required.