DEMOCRATIC EVOLUTION OCCURING,
DEVELOPING NEW RULES
Ballot weights assure each voter a fair and limited share of power. MinO assures each winner has a certain breadth of support. We need some way(s) to assure a high utility value per dollar -- something governments and other large bureaucracies often do poorly. Current research on STA options seeks to maximize the value of results for all interest groups. Here is a statement of the dilemma and some examples of STA options.
Perhaps requiring MinO puts too much emphasis on broad popularity and collective decision making over intense popularity and independent action. The MinO system divides a voter's weight among his top choices. There is no effective difference between his first choice and his fifth. This is a crude measure of utility because it treats all of his high preferences the same. Switching the ranks of 2 high preferences makes no difference in their fates. Is the rule correct if it suspends item Bwith, say, 8 firsts rather than Gwith 9 seconds?
If MinO is high, the fraction of weight a ballot offers to its top choice is low. (Offer = $ vote / MinO.) The ballot then offers a little weight to many items. The top choice is not hurt by the other items because its weight is reserved -- as long as its popularity is not so weak it gets suspended.
8) There are 4 basic ways to time the collection of contributions. The timing may effect the utility value of the results. a) Immediately collect contributions when the item reaches MinO; then declare the item closed. Since these are the ballots that enthusiastically gave high ranks to that item, this way probably leads to a high average contribution and budget. If so, then few items will be funded. Also a few voters will contribute a lot of their weight to each winner. The next 3 methods often lower item budgets because a voter who gives a low rank probably gives a low $ vote. They also catch free riders who rank sure losers as their top preferences -- so as not to spend weight on the early winners.
b) Continue collecting late offers made to an item that has already reached MinO and has taken contributions. Early contributors will get some weight back. (Recall that each rep's contribution was her $ vote / actual number of contributors. If her $ vote is divided by a larger number of contributors, her contribution is smaller.)
c) Delay collection until the end of the tally. Letting a ballot keep its weight till the end holds open its power to fund a high-ranking suspended item, B, and drop lower-ranked winnerG. But we know that several other ballots ranked G above B because G won before B did. (If MinO is proportional to cost and B costs more than G, we can say G has more contributors relative to cost than B does.)
[ d) Release suspends $ votes reserved for sticky items. A "sticky" item can almost but not quite reach MinO. A "stuck" ballot's weight remains reserved for such an item. The item gets eliminated late in the tally. But by then many of the ballot's other top preferences have also been eliminated. So the voter's weight goes to a very low preference or is not spent at all. The tally is run again and releases (suspends) votes reserved for sticky items (previous losers) 1 item at a time.
[[ Item C may have to be suspended repeatedly as votes for other items are released and ballots transfer weight down to C. Each offer is $ vote / MinO or current offers whichever is larger. [ This must be calculated repeatedly. When the number of offers goes up, the size of each offer goes down, leaving a ballot with money for more offers, so the number of offers goes up... ]
[ Each loser may yet win, but the voter's weight also may help his other top choices. When a ballot's losing votes all have been released, its weight is all offered to winners of the previous tally or contributed to new winners. When no weight is reserved for losers on any ballot, then winners of the previous tally may win. If the list of winners is not the same as the previous tally's winners, the process may be repeated.
[ Like collecting late offers, this process catches free riders. Collecting late offers is easier to explain but releasing losers might be faster or more fair. They can work together.
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The utility problem again is this: Perhaps MinO gives too much emphasis to broad popularity over intense popularity. There is no effective difference between a voter's first choice and his fifth. Is the rule correct if it suspends item Bwith, say, 8 firsts rather than Gwith 9 seconds?
4) In terms of point voting rules, MinO effectively sets an upper limit on the point scale. In our example where MinO = 20, the maximum vote is 1 / [20]th of the points needed to win funding. Every ballot gives that maximum to as many top prefs as it has points for.
3) The last item a ballot has any weight for usually gets only a partial vote or offer. The ballot's top choice could be given a double vote. That would count as offers from 2 ballots. The ballot will have to double the weight it offers. If that vote gets suspended, the doubling moves to or is shared with the next preference. (Otherwise doubling acts like a plurality rule.) Smaller partial votes could be added to the second, third, and forth choices. All of this is arbitrary. It does not accurately measure preference intensities. But allowing votes to be tripled or quadrupled might be inappropriate; limiting the maximum score fits the rule's emphasis on broad popularity and collective decision making.
Here are 5 options:
1) Diminish high scores to discourage exaggeration. Square root rule created by Hylland and Zeckhauser in the 1980s.
2) Modify all scores to do 1 above and to spread them out. Standardized Scores created by Samuel Merrill in the 1980s.
3) Assign preset scores to ranks to do 1 and 2, and to give all ballots an equally emphatic strategy. Borda points created by Borda in the 1780s.
4) Make all scores equal 1 to do 1, 2, 3, and to value broad popularity over intensity. Approval Voting created by Stephen Brams in the 1970s.
5) Charge a higher rate of weight for high scores. Incentive Revealing Devices created by Vickery, Clark, Tideman, and others from the 1960s through the 1970s. .
[ The next 3 options are made moot by previous features. All are helpful for understanding STV elections and are available in Political Sim. But most readers can skip them. .
[ 9) After an item wins, revive all eliminated items so the winner's excess funds may transfer to them. Made moot by suspend. ]
Revive, or Suspend and Release may help STV and LER elect the most popular candidate in an interest group even if she is sandwiched by other candidates.
[ 10) Ignore an item that has no contributions. No items are helped by eliminating it. It might get enough transfers to win later. Inherent in the $ vote system. ]
[ 11) Each ballot gives some phony dollars to its next (2nd) choice. These dollars only help an item to avoid elimination, not to win. They tell the voting rule which items are likely to get real contributions soon. This tends to help central options and not the fringe. (To help a lower choice win while the top has a chance would use up weight and may lead the top choice to lose for lack of that weight. It also encourages punishing votes.) Made moot by $ votes. ]
[ 12) An alternate winner's total of weights when suspended repeatedly is more than its cost. It did not win because the order of wins kept it from holding all of these offers at once. After item B. was first suspended, some supporters contributed weight to their lower preferences. Later, other supporters transferred and offered some weight to B. B never had enough weight all at once to win. And yet on some ballots, B ranked higher than some of the items contributed to. Those voters might be happier if B won and their lower preference, G, lost. But other G contributors might not like that change.
[ An alternate winner can be made golden, immune from suspension, before a new STA tally. The resulting set of winners is compared with other sets of winners with different items made golden. The problem in such comparisons is asking each voter something like, "Would you rather win your first and forth preferences or your second and third?"
[ The easiest method arbitrarily assigns points to each voter's top [8] choices (perhaps 50 for first, 42 for second, and so on). A more accurate method lets voters cast points instead of ranks. The voter decides how many points each item is worth compared to his first choice. A ballot's points are ranked for STA tally steps so there are no new incentives for strategic voting. (Utility voting rules also ask voters for point scores, but personal points for STA are compared only with scores on the same ballot. This avoids the problems in comparing what one voter means by 10 points with what another voter may mean.)
[ The voter's points for a set of winners are totaled. Condorcet's rule picks the set that most voters prefer over any other. This does not lead to funding only majority projects because all sets include items funded by minority votes. (It reduces free-ride incentives because in pairwise tests, a free-rider's ballot tends to support sets with insincere top ranks, not sets with free rides.) The computer tally could produce 5 or 6 sets of winners for the voters to choose from in a Condorcet runoff.
[ A higher preference should not be hurt by contributions to lower preferences. The high preference's $ are reserved -- unless it has been suspended. But here is another pattern of "alternate winners": A high preference is suspended. That money is released and offered to a lower choice. If the lower choice wins and then the suspended item wins, the $ in effect are taken from a reserved middle choice which was strongly supported, never suspended, and which might have won if the order of suspensions and wins had not helped this voter's lower choice.
[ A program can find an item that was skipped over; count how many supporters it had and how much was paid to their lower choices. If that amount is enough to fund the skipped item, then its supporters would prefer it. A second tally could make the high choice golden until the middle choice (the alternate winner) is funded. But funding the skipped item might un-fund its supporters' lower choices -- which may be other voters' top choices! Here again the program or the voters could choose between sets of winners.
The by-laws require each item to win funds from a minimum number of reps: one-tenth to one-third -- the same as the fraction of the budget voted by each rep. This also becomes the maximum fraction that 1 item can win.
Each item's sponsor suggests a funding level for it. The by-laws specify a range of allowable $ votes such as 25% to 300% of the suggested amount. The sponsor may set a narrower range or a fixed price.
An item must win support from a large minority. It is funded at the average amount they voted for it.
An item can win more than enough supporters. Then those who voted to give it a small budget are not among its top supporters. They are hurting themselves if they do not move their funds to raise the budgets of some other item(s). The excess low votes should be transferred.
[ * To understand this new funding rule, it will help to understand 2 old election rules: bloc vote and limited vote. Both are used in "at large" elections. For example, a 5 seat city council in which all candidates compete in 1 city-wide district. The candidates who get the most votes win. Bloc vote lets a voter cast as many votes as there are seats to fill. He may give only 1 vote to a candidate. A majority group with 5 candidates for 5 seats wins all 5. No other candidate can win more votes. Limited vote lets a voter cast fewer votes. Each voter in a 5 seat district might cast 3 votes. If the majority gave all its votes to 3 candidates they would win that majority -- but not all of the seats. Limited vote often results in proportional representation. But if the majority's votes were evenly divided among 5 candidates, most could lose. Plurality rules that lack candidate elimination and vote transfer leave a group split by too many candidates. ]
MFP's process avoids plurality-rule problems. The process is a sequence of votes, requiring progressively higher numbers of supporters. After each step, the item with fewest supporters is eliminated, like the weakest candidate in an STV tally; reps then transfer their allocations from the loser to the remaining items.
Most point-voting rules offer easy strategies: the punishing votes and exaggerations explained in the pages on elections. But MFP has conflicting incentives. A version of this has been used for several years by a 100 voter group in Virginia. They find the incentive to exaggerate for one's top preference is more than off-set by the incentive to spread out one's vote and create as many winners as possible. Some ballots have several minimum votes but maximum votes are few. Most votes are not at the extremes.
MFP Variations Number Minimum Voter's % Rule of Groups % in Group of Budget MFP33 3 33 33 MFP25 4 25 25 MFP20 5 20 20 MFP11 9 11 11
Voters usually won't form such distinctly separate groups. Instead, interest groups will overlap on many proposals. Conducting an MFP Vote
This process is like the Median Voter Process.
Set by-laws for the voter's percentage of the budget and the range of allowable $ votes.
Design ballots listing items with their suggested and minimum amounts. Leave several columns for $ votes and revisions.
Introduce MFP: "Each item needs at least [25] supporters to win. Items with less than [25] will be eliminated, 1 at a time. Move your $ from losers to remaining items."
Tally how many reps support each item on the first vote. Track additional supporters after each elimination.
Find the decisive [25]th voter for each item. Remind reps with lower $ votes to move their funds and ask them to name any newly-supported item so its tally can be increased to avoid elimination.
Eliminate the weakest item. If several items tie for elimination: A) Ask reps who voted for 2 or more of the tied items, "Which of those would you drop?" Eliminate the 1 with the weakest support. B) Use Condorcet's rule. Eliminations force reps to move $ votes more often than in MVP.
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Twenty people picking 5 pizzas from 30 on a menu could use another rule like STV. The Joint Allocation Rule adapts STV for collectively buying personal goods in bulk lots.
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The January '97 version of Political Sim introduced 3 election rules for simulation research. Economic simulations define "utility" as proximity. The Maximum Utility Candidate (MUC) is the 1 whose total of distances to all voters is the shortest. That is the candidate closest to the average voter. The Maximum Utility Series (MUS) fills the council with that candidate and the next best and so on. The Maximum Utility Group (MUG) elects the council that best distributes representation so each voter has a nearby rep. The Maximum Utility Ensemble (MUE) is analogous to LER: the MUC takes the place of the Condorcet winner as chair and MUG takes the place of STV in electing the reps.
MUE can adapt to be an allocation rule like LAR. If an item wins funding, its fund will be its average $ vote. MUS uses [15]% of the budget; MUG uses the rest. For MUG, a social-utility score must be tallied for each set or combination of projects that fit within the budget. Each ballot searches a set for favorite items totaling [20]% of the budget. The ballot's scores for those items are totaled and added to the set's score.
If an item is not in the top [20]% of items on at least [20]% of the ballots, then it does not met the MinO requirement. The 1 with the fewest supporters is dropped from the set and the set's score is calculated all over again. The set with the best score wins.
The most obvious problem with MUG is the time it takes to test every possible set of winners.
All utility rules have a major problem: By moving a large distance to 1 side, extremist voters have a large effect on MUC's winner -- more than on Condorcet's. MUC elects the candidate closest to the average voter. Condorcet's rule elects the candidate closest to the median voter. (A median does not change as extremes become more extreme.) This shows the utility rule's vulnerability to manipulation by exaggerated and punishing votes. Of course MUG is not nearly as good as STV, the rule most resistant to manipulation. When reps vote strategically the outcome of a utility rule cannot reach it high potential utility value.
Merrill's Standard Score Voting Rule minimizes extreme votes. It forces each ballot's scores toward a bell-curve distribution with a standard deviation of 1. A ballot with scores clustered at the center or extremes becomes more spread out. The ballot needs to be on a computer because a rep needs to see both her raw scores and her standardized scores. Political Sim offers players Standard Score voting on thermometer charts as a way of selecting the election rule. This might lead to voting rules better than LER and LAR, but for now it is less practical.
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Each ballot acts as an agent trying to maximize the value of the outcome for its voter. Input varies according to the voter's preferences. An agent has less information than its voter about his preferences but more time and information about other voters. MVP agents, for example, search for other agents to negotiate vote trades. LAR agents search for others to form the minimum needed for winning. Simulation techniques can evolve new agents through differentiation and selection of successful ones.
Rank $ Allocation Tens Ones Rank Item name $ Thousands Hundreds Tens ooooooooo ooooooooo 5 sdf 6770 ooooooooo ooooooooo ooooooooo ooooooooo ooooooooo 3 bskt 550 ooooooooo ooooooooo ooooooooo ooooooooo ooooooooo 12 fzdt 750 ooooooooo ooooooooo ooooooooo
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Political scientists, mathematicians, and economists have tried for decades to create rules for Proportional Allocations (PA). But all have failed, often because a coalition could manipulate the results. (In fact, several researchers have found mathematical proofs that no voting rule can promise to always meet various reasonable criteria; so no rule can be perfect.) Still, in order to buy public goods such as roads and schools, we need to find the best rules possible. The best ways to compare voting rules are case studies and computer simulations like Political Sim. .
LAR versus MFP: LAR increases the number of people who share the cost of a popular item, so it costs each person less; increases the average number of items a person contributes to; increases the number of top-ranked items that low bidders contribute to; decreases the $ per item. MFP lets voters deal with 2 of a kind.
The Minority Funding Process is quite adaptable, but its repeated votes are time consuming and demand voters' close attention. In the Loring Allocation Rule, voters simply rank the options, but the current version lets sponsors, not voters, set an item's budget and the tally is complicated. Further research, including computer and workshop simulations of voting, is needed to evaluate, compare, and develop rules for proportional allocations. .
Return to funding projects, LAR.
© 1997 Robert Loring Reprints are permitted.