Shapley Value Calculator

This is the simplest version of a program which computes the result of an election, under the Proportional Approval Voting method.

It takes a csv (comma separated value) file, with the same format as this one, which might be produced by a Google Forms like this one.

It computes the result using client-side JavaScript, which means that all operations are run in your browser, as opposed to in a server which is not under your control. In effect, all this webpage does is provide you with a bunch of functions. In fact, you could just load this page, disconnect from the internet, upload your files, and you could still use the webpage to get the results you need.

List of examples

+Example 1: Alice and Bob and both necessary to produce something which has value 1500. Alice is player 1, Bob is player 2. +

+Example 2: Alice and Bob are each individually responsible for two different projects, each of which has value 1000. Alice is player 1, Bob is player 2. +

+Example 3: Newton and Leibniz invented calculus at the same time. It has a value of 100, in arbitrary units. Assumption: Nobody else could have invented calculus. Newton is player 1, Leibniz is player 2 +

+Example 4: Netwon invented Calculus. Leibniz, mad with envy, pretended that he also invented calculus at the same time. Newton is player 1. Lebniz is player 2. +

+Example 5: Suppose that AMF will spend $1m on a net distribution. As a result of AMF’s commitment, the Gates Foundation contributes $400,000. If AMF had not acted, Gates would have spent the $400,000 on something else, half as valuable. AMF is player 1, Gates is player 2. +

+Example 6: Suppose again that AMF commits $1m to a net distribution. But if AMF had put nothing in, DFID would instead have committed $500,000 to the net distribution. Now, DFID commits that money to something half as valuable. AMF is player 1, DFID is player 2. +

+Example 7: 7 people boil a goat in their mother's milk, independently and at the same time. According to the Kabbalah, this has terrible implications: -1000 value is lost. Suppose that all the damage is done once the first deed is done. +

+Example 8: Suppose that there was a position in an EA org, for which there were 6 qualified applicants which are otherwise 'idle'. In arbitrary units, the person in that position in that organization can produce an impact of 100 utility. The organization is player 1, applicants are players 2-7. +

+Example 9: A small Indian state with 10 million inhabitants spends $60 million to vaccinate 30% of their population. An NGO which would otherwise be doing something really ineffective, comes in, and by sending reminders, increases the vaccination rate to 35%. They do this very cheaply, for $100,000. The government is player 1, the indian state is player 2. What if, instead, the NGO would have done something equally valuable? +

+Example 10 1: Same as Example 9, but now there are 6 government subagencies, each of which we consider as a distinct agent. The NGO is player 1, government agencies are players 2-7. +

Shapley Value Calculator

'; +echo "

"; +switch ($example) { + case 1: + echo "Example 1: Alice and Bob and both necessary to produce something which has value 1500. Alice is player 1, Bob is player 2."; + $numPlayers = 2; + $getCoalitionNum = array(0,0,0,1500); + break; + case 2: + echo "Example 2: Alice and Bob are each individually responsible for two different projects, each of which has value 1000. Alice is player 1, Bob is player 2."; + $getCoalitionNum = array(0,1000,1000,2000); + $numPlayers =2; + break; + case 3: + echo "Example 3: Newton and Leibniz invented calculus at the same time. It has a value of 100, in arbitrary units. Assumption: Nobody else could have invented calculus. Newton is player 1, Leibniz is player 2"; + $getCoalitionNum = array(0,100,100,100); + $numPlayers =2; + break; + case 4: + echo "Example 4: Netwon invented Calculus. Leibniz, mad with envy, pretended that he also invented calculus at the same time. Newton is player 1. Lebniz is player 2."; + $getCoalitionNum = array(0,100,0,100); + $numPlayers =2; + break; + case 5: + echo "Example 5: Suppose that AMF will spend $1M on a net distribution. As a result of AMF’s commitment, the Gates Foundation contributes $400,000. If AMF had not acted, Gates would have spent the $400,000 on something else, half as valuable. AMF is player 1, Gates is player 2."; + $getCoalitionNum = array(0,1000000,200000,1400000); + $numPlayers =2; + break; + case 6: + echo "Example 6: Suppose that AMF commits $1M to a net distribution. But if AMF had put nothing in, DFID would instead have committed $500,000 to the net distribution. Now, DFID commits that money to something half as valuable. AMF is player 1, DFID is player 2."; + $getCoalitionNum = array(0,1000000,500000,1250000); + $numPlayers =2; + break; + case 7: + echo "Example 7: 7 people boil a goat in their mother's milk, independently and at the same time. According to the Kabbalah, this has terrible implications: -1000 value is lost. Suppose that all the damage is done once the first deed is done."; + $numPlayers =7; + $getCoalitionNum = array(0); + for($i = 1; $i<128; $i++){ + array_push($getCoalitionNum, -100); + } + break; + case 8: + echo "Example 8: Suppose that there was a position in an EA org, for which there were 6 qualified applicants which are otherwise 'idle'. In arbitrary units, the person in that position in that organization can produce an impact of 100 utility. The organization is player 1, applicants are players 2-7."; + $numPlayers =7; + $getCoalitionNum = array(0); + for($i = 1; $i<128; $i++){ + if($i<=64){ + array_push($getCoalitionNum, 0); + }else{ + array_push($getCoalitionNum, 100); + } + } + break; + case 9: + echo "Example 9: A small Indian state with 10 million inhabitants spends $60 million to vaccinate 30% of their population. An NGO which would otherwise be doing something really ineffective, comes in, and by sending reminders, increases the vaccination rate to 35%. They do this very cheaply, for $100,000. The government is player 1, the indian state is player 2. Exercise: What if, instead, the NGO would have done something equally valuable?"; + $numPlayers =2; + $getCoalitionNum = array(0,3000000,0,3500000); + break; + case 10: + echo "Example 10: Same as Example 9, but now there are 6 government subagencies, each of which we consider as a distinct agent. The NGO is player 1, government agencies are players 2-7."; + $numPlayers =7; + $getCoalitionNum = array(0); + for($i = 1; $i<128; $i++){ + if($i<126){ + array_push($getCoalitionNum, 0); + }else if($i==126){ + array_push($getCoalitionNum, 3000000); + }else{ + array_push($getCoalitionNum, 3500000); + } + } + break; + default: + $example = -1; + break; + +} +echo "

"; +echo "

'; +for($n=1; $n <=$numPlayers; $n++){ + echo "The Shapley value of player ".$n." is: ".$Impact[$n-1]/$numPlayers."
"; +} +echo '

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Shapley Value Calculator

'; +for($n=1; $n <=$numPlayers; $n++){ + echo "The Shapley value of player ".$n." is: ".$Impact[$n-1]/$numPlayers."
"; +} +echo '

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Shapley Value Calculator

'; + $payout = ($sumContributions*$getMultiplier/$numPlayers); + echo 'Payout = Sum*Multiplier/ Number of Players = '.$payout; + echo '

Proportional Approval Voting MVP

What is this? How does this work?

List of examples

Shapley Value Calculator

Also of interest:

Shapley Value Calculator

Also of interest:

Shapley Value Calculator

For each player, what is the difference between the payout and the Shapley value?