Different uses for voting need different types of voting.

Notes on voting rules for setting budgets

Median Voter Process

Simple equipment to help a budget vote
During a Median Voter Process (MVP), each rep shows how she would "allocate" the expected revenue. She is limited by that amount: if she increases one budget, she must cut that money from others.

An agency will get the median or middle amount voted to it. Half of the reps want to give it more; half want to give it less. So the median is the only amount with majority support.

MVP Qualities

Unlike an average, a simple median gives voters no incentive to exaggerate. A vote ten dollars above the median has the same affect as a vote ten million above. But if vote trading occurs, a rep can drop a few budgets to the minimum allowed and use that money to raising her votes for budgets that her trading partners want raised. Alex might say to Bobby, "I'll raise my previous low vote for your committee if you'll raise yours for my committee." This is time consuming and the results are not very rational because many changes to the budgets depend on who is quickest to find a deal, not on any depth thinking about the effects.

If there is a disciplined majority group, they can determine every budget and other reps can influence nothing. So, like the common agenda process and other majority rules, MVP can result in skewed power -- but at least a mere plurality cannot control MVP funds. When there is no ruling majority, all reps have some power, making the results roughly balanced, central, and stable.

An omnibus bill can entice a majority of reps to support a collection of items, each of which has only minority support. Sadly, such bills often include wasteful "pork" -- so councils should make them easy to trim. The MVP process cannot prevent that unhealthy temptation, but it keeps a tight lid on the pot which raises the pressure on budgets and cooks some of the fat out.

Notes: Expected revenue may include sales of government bonds (which many investment portfolios depend upon for stability) and budget items may include various tax rebates. MVP also works for private organizations which distribute votes by wealth: a rich voter gets more than one vote for each budget item.

MVP Formulas

Those with a feeling for math will note that the sum of the medians for all departments probably will not equal the overall budget. To fix that fairly, each department's median can be multiplied by the expected revenue divided by the sum of the medians. This is just the department's median minus a fraction of itself.

In math terms, let B = Budget, i = item, M = Median, and T = Total.
Let B(i) be the budget for item i and M(i) be the median vote for i; let T(m) be the sum of all M(i) and R be the revenue or funds available. This adjustment formula is written:

B(i) = M(i) * ( R / T(m) )

Which says the Budget of an item equals the Median of the item times the expected Revenue divided by the Total of all medians.)

(On each ballot, a similar formula:

adjusted vote for i = vote for i * (R / sum of ballot's votes)
automatically ensures each rep does not exceed the overall budget. Voters do not have to do the arithmetic.)

Anton Sherwood suggests another adjustment formula (M-n) and an analogy: To adjust the overall budget use each department's nth vote above or below the median vote. On a council of 99 reps, a median is the 50th largest vote for a department. If the sum of the medians exceeds the revenues, then each department gets the amount of its 49th-largest vote. That way 50 reps say each department should get more, and 48 say less.

Thus MVP in this form can require super majorities to support each department's budget. This favors items with a soft consensus, meaning many votes near the median. (If vote trading raises total budgets over revenue, then all budgets drop down one voter, taking away the effect of one vote trade. This hurts mainly items which have not received trades.)

In math terms, let B = Budget, i = item, m = median and T = Total.
Let B(i,n) be nth lowest amount chosen for budget item i; let T(n) be the sum over i of B(i,n). Let k be the highest number such that T(k) is less than or equal to expected revenue. If each budget item is enacted as B(i,k), then the budget is balanced, with no deficit but possibly a small surplus.

A Brick Analogy

Imagine that a rep is given a brick for each budget item. She writes her proposed budget for the Labor Department on her Labor Department brick. The Labor Department bricks from all 435 reps are stacked with the lowest proposed budget at the bottom and the highest at the top. Each department or agency has its own stack.

We throw away the top 217 (=435 divided by 2) bricks on each pile, because the numbers on them represent spending that does not have majority support.

Look at the new top layer of bricks and add up their numbers. Is the total more than expected revenue? If so, throw away that layer and try again -- until you find a balanced budget. (Readers may find it more convenient but less invigorating to use a stack of 3 by 5 cards or a tally program.)


You may download free, open-source software for both MVP voting rules on a 95KB spreadsheet for Microsoft Excel 7 or higher.

Vote Trading

The council members might negotiate: If P voted at or below the median on 1 of Q's favorite items, and Q voted below the median on 1 of P's favorites, they could agree "I'll raise yours if you'll raise mine." Of course a rep must be skilled at bluffing and negotiation to maximize her results.

MVP ballots do not measure the intensities of reps' opinions (as political cards do); but if reps have time, they may trade votes to help the things they care about most. A rep may show her certified first ballot to trading partners. She then inks in her second ballot together with each trading partner.

The following tally shows opportunities for vote trading -- any pair of reps could raise each other's favorite. The adjustment then would lower the third item to less than one.

MVP with a budget of $9
    Items     3 Ballots  
$3 total
$9 total
$3 total

This polarized electorate makes the addition and multiplication easy, but it is too bizarre to show how Sherwood's adjustment can work. In large groups, many votes often are near the median so any ballot can be removed with little affect on the item's budget by either adjustment formula. That shows the decision is strong, not by chance. Adjustment M-f reduces all items; adjustment M-n reduces those with few votes near the initial median.

Take a council with 15 reps from several parties. The Blue's have 3 reps and the Grays have 6. Neither party has a majority so neither can fund anything on its own. The Blue reps might offer to give $100 each to a department favored by the Grays. The Grays can match that with $100 each to make its median $100. The Gray reps might be willing to give Blue's favorite department only $50 each, $300 total in exchange for Blue's $300. But the median would be only $50 so the Blues might negotiate with other parties for a better deal.

If there is another party with 6 reps, all 3 parties have equal power since any 2 can form a majority of 6 + 3. The small party is as necessary as the large. Thus under MVP, power is not always proportional to party size. Influence Points do better and fair-share spending does much better.

MVP Network Voting Software

This simple program lets up to 9 voters use MVP to set budgets, trade votes and watch the changes as they happen. Instructions for installing the 9 ballots and tally sheet are on Read_Me.doc. The zipped file is 75KB. Download ballots and tally program.

MVP by Show of Hands

Design ballots.
List agencies with several columns for $ amounts.
Shade or underline every second line.
Number the agencies to help voters find them.
Leave blank lines for new items or splits.
Put a line for "Totals" at the bottom.
Number the ballots to help count the voters.

Present proposals:
The meeting coordinator reads the mission statement before or after presentations.
Agency sponsors suggest several spending levels and their benefits.

Introduce MVP:
"You each have the entire budget, [24,000] dollars.
Divide that among the [19] departments.
Each agency will be funded with the median amount voted for it.

Find decisive voters:
Write a low budget number for the agency.
Say "Raise your hand if you gave money to the agency.
Put your hand down when this number is more than your vote for the agency."
Raise the number.
Stop when the [8th] hand goes down.
Ask that voter, "What did you budget for this?"
Write that amount on the board.
Repeat for each agency.

A vote above the median for an agency is excessive, wasted.
Reps may move excess funds to raise other budgets.

If there is time for vote trading, perhaps all ballots should be posted. Vote trading lets reps help the things they care most about.

Collect and Verify the Ballots:
Enter each ballot on a simple spreadsheet.
Total a ballot's votes for all items.
Adjust the Vote for each item on this ballot so the ballot's new total equals the overall Budget.
          adjusted V(i) = V(i) * (B / T(1--n) )
Which says the adjusted Vote for item i equals the vote marked on the ballot times the overall Budget divided by the Total of all votes marked on the ballot.

Find median vote for each item.
Total the medians for all items.
If their total exceeds the overall budget, adjust each item using one of the two MVP formulas above.  Hylland & Zeckhauser rule

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