Loring Allocation Rules

The Loring Allocation Rule (LAR) makes comparison of results routine by holding a second vote to pick the final set of winning projects from 5 or 10 sets.  Some sets come from variations in the vote quota for MMV and the ratio of funds allocated by a centrist tally rule or a fair-share rule.  But some sets of winners may be the results of other fair-share allocation rules.  (Non-proportional rules may not be used because majorities often would select the non-proportional sets and keep all power rather than share it more democratically.)

Condorcet + STV

LAR builds on the foundations of the Condorcet and STV rules, just as the Loring one-winner and ensemble rules do. Returning to an earlier case, LAR voting could control a co-operative journal, video, or Internet channel. This lets the subscriber-voters directly allocate funds for features, columnists, supplements, and cartoons; serials, specials, sports, and news. All voters get all winners.

Some of the comics' fund is awarded by a central Condorcet Allocation System (CAS). The comics are ranked as first Condorcet winner, second, third and so on. The CAS part of the budget should be enough to fund several broadly-popular comics. A winner receives the median of the preferred budgets given it by voters but supporters lose no MMV weight. The rest of the budget then goes to the MMV tally.

(The Schulze method and Tideman's Ranked Pairs each create a ranked list of winners. So they are good rules to use for CAS.)

Funding some Condorcet winners before MMV reduces the free-rider incentive. For example, Voter: "I know Calvin and Hobbes. is going to win. Why should I waste part of my weight supporting it?" Pollster: "If it is sure to win, it probably will during CAS. Supporters' MMV shares won't be reduced. You probably cannot predict later winners of MMV voting. So you just need to think about rating your honest preferences. " Then software easily handles the tally, including any MMV options.

The most popular projects win funding before FS. Thus majority voting funds basic needs while the fair-share rule decides only which extras to buy. Free rides are not a great concern because no one gets free basics while saving money for extras. This reduces the reward for free riding and all that goes with that: bluffing, cynicism, and the under funding of those shared items.

A single ballot serves both CAS and MMV tallies because both rules ask voters to give first preference to the most cost-effective option, 2nd to the 2nd most cost-effective and so on.

(CAS might be replaced by MMV with a very high quota, perhaps over 50%. Voters who support the winners of this preliminary tally would be charged less than the full costs of the winning items.)

How many people should be required to back a project paid for with public funds? In setting quota, consider the shares of votes in current interest groups. Even a quota of 50% cannot make MMV a pure majority rule; because each voter has a share of money, the majority cannot have it all. But a high quota can leave a minority's money unspent, useless.

(An organization whose charter, constitution, or by-laws require majority support for allocations can use CAS and include "Fund no more" on the ballot. An item that does not win a majority over "Fund no more" will not be funded.)

The tally software may create 4 or 5 sets of winners. Each set would use a different ratio of central CAS to distributed MMV funds and size(s) of quota. All sets would include some items funded by minority ballots. Voters would have the final choice in a Condorcet tally selecting the most popular set.

But Condorcet is a majority rule and those have often failed to protect minority rights. So the minority's right to discretionary funds must be protected in the by-laws by setting a minimum amount for the MMV share of funds and an upper limit on quota.

A group with few people or little money might decide to allocate half or more by a central rule. But a city would probably allocate most discretionary funds by a fair-share rule.

Evaluating of sets of winners

Table 3 compares 2 sets of winners by listing each winner's budget times the number of voters who ranked it as a first or second choice.

Evaluations of Ballots with Scores

Utility1 Sum for all ballots: contribution to winner × ballot's score for it.  No utility added for items which ballot did not contribute to.
Utility2 Sum for all winners and all ballots: winner's budget × score on each ballot.  No utility added for items which ballot did not rate.
Any method of summing utility scores given by diverse voters is highly questionable because of the wide variation in voter definitions of "100 points" or "grade B".
Utility Curve utility values from curves like those on the MMV ballot.  A ballot's utility score adds areas for top preferences which won.
Utility = - item's X [position along x] / sum($Votes) [width of x axis] + 2
A straight line from (2 pts,$0) to (0 pts,sum $Votes).
All $Votes can be much more than budget.
No utility added for unranked items or lacking $Vote.
[We cannot know how far down the curve to score them.]

Equity: 2 graphs for each set of winning projects:
Sort voters by the total Utilities of each
1) Utility up Y axis.  Voters along X axis; voter with the lowest utility on the left.
Readers can easily compare the height of the poorest voter's column to that of the richest voter.
2) Lorenz curve showing the running total of voter utility scores.  A Lorenz curve is concave upward.  On the left, the line is rather flat as it adds small utilities for poor voters.  On the right the line points up sharply as it adds utility scores for rich voters.  The more concave it is, the less equal the results were.  If each voter won the same amount, the line would be straight.  This may give less emphasis to extremes than graph 1.

100%|                   +*
    |                 + *
  D |               +  *
  O |             +   *
  L |           +   *
  L |         +   *
  A |       +   *
  R |     +  *
  $ |   + *
 10%| +*                 .
    10%     VOTERS      100%
+ Perfect equality
* Actual winnings

The fundamental qualities of LAR come from 2 works of genius: the Condorcet and STV rules.  Although the new rule is untried, its building blocks are the 2 most highly-regarded voting rules.  The key question is not whether LAR will work, but whether a group dares to give some spending power to minorities.

Most groups need budget-setting rules only once a year.  The Hylland-Zeckhauser and Loring Allocation Rules can handle these difficult decisions with efficiency and fairness, producing stable, high-value results.