in javascript, say i've got a hash of candidates and a list of ranked ballots. The hash will be an object where the members have a key which is typically a single letter (and is the candidates' short name) , and a value which is a longer string, which will be the candidates full name. The ballots will be will be arrays of arrays of strings, where each string is the short name (key) of a candidate. they will be ordered with the first being the voter's first choice. If a candidate isn't listed, they are least preferred. there will never be a candidate duplicated in a ballot. for starters, can you generate a bit of sample data in this format? please have it in a single object, with members ballots and candidates.
Sure! Here's an example of a JavaScript object containing sample candidates and ranked ballots:
javascriptCopy codeconst electionData = {
candidates: {
A: "Alice Johnson",
B: "Bob Smith",
C: "Charlie Brown",
D: "Diana Ross",
E: "Eddie Murphy"
},
ballots: [
["A", "B", "C", "D"],
["B", "A", "D", "C"],
["A", "C", "B", "D"],
["E", "B", "C", "A"],
["D", "C", "B", "A"],
["B", "D", "A", "C"],
["C", "A", "B", "D"],
["A", "B", "D", "C"],
["D", "B", "A", "C"],
["C", "E", "A", "B"]
]
};
In this example, the candidates object has 5 candidates with their short names (keys) and full names (values). The ballots array contains 10 ranked ballots, each represented as an array of short names in the order of the voter's preference. Note that not every candidate is listed on every ballot, which implies that any unlisted candidates are least preferred by the voter.
they don't all have to list all candidates. please have some with fewer candidates listed
Sure! Here's an updated version of the election data object, including some ballots with fewer candidates listed:
javascriptCopy codeconst electionData = {
candidates: {
A: "Alice Johnson",
B: "Bob Smith",
C: "Charlie Brown",
D: "Diana Ross",
E: "Eddie Murphy"
},
ballots: [
["A", "B", "C", "D"],
["B", "A", "D"],
["A", "C", "B"],
["E", "B", "C"],
["D", "C", "B"],
["B", "D"],
["C", "A", "B", "D"],
["A", "B"],
["D", "B", "A"],
["C", "E"]
]
};
In this example, some ballots include fewer candidates than the total number of candidates available. This represents voters who have not ranked all candidates in their preference order.
can you produce a function that will, given a set of candidates and ranked ballots as shown above, remove a given candidate? It should produce an all new object, rather than altering any of the members of the passed in electionData object.
Certainly! Here's a function called removeCandidate that takes an electionData object, a candidateToRemove short name, and returns a new object with the candidate removed from both the candidates and the ranked ballots:
javascriptCopy codefunction removeCandidate(electionData, candidateToRemove) {
const newCandidates = { ...electionData.candidates };
delete newCandidates[candidateToRemove];
const newBallots = electionData.ballots.map(ballot => {
return ballot.filter(candidate => candidate !== candidateToRemove);
});
return {
candidates: newCandidates,
ballots: newBallots
};
}
Here's an example of how to use this function:
javascriptCopy codeconst updatedElectionData = removeCandidate(electionData, 'E');
console.log(updatedElectionData);
This function first creates a shallow copy of the candidates object using the spread operator and removes the specified candidate. Then, it creates a new array of ballots with the specified candidate filtered out. Finally, the function returns a new object containing the updated candidates and ballots.
now make a function called getPluralityWinnerOrLoser, that takes an electionData object and a "findLoser" argument, and returns an object that contains a member "selected" that is an array of all winners (or losers, if findLoser is true). A winner is the candidate with the most first place votes. A loser is the candidate with the least first place votes. If there is a tie, there will be more than one. There will always be at least one candidate in the selected array.
Here's a function called getPluralityWinnerOrLoser that takes an electionData object and a findLoser argument, and returns an object containing a member "selected" that is an array of all winners or losers, based on the findLoser parameter:
javascriptCopy codefunction getPluralityWinnerOrLoser(electionData, findLoser = false) {
const firstPlaceVotes = {};
// Initialize the firstPlaceVotes object with the candidate keys and zero votes
Object.keys(electionData.candidates).forEach(candidateKey => {
firstPlaceVotes[candidateKey] = 0;
});
// Count the first place votes for each candidate
electionData.ballots.forEach(ballot => {
if (ballot.length > 0) {
const firstPlaceCandidate = ballot[0];
firstPlaceVotes[firstPlaceCandidate]++;
}
});
// Find the highest or lowest number of first place votes
const voteValues = Object.values(firstPlaceVotes);
const targetVoteCount = findLoser
? Math.min(...voteValues)
: Math.max(...voteValues);
// Find the candidates with the highest or lowest number of first place votes
const selected = Object.keys(firstPlaceVotes).filter(
candidateKey => firstPlaceVotes[candidateKey] === targetVoteCount
);
return {
selected: selected
};
}
Here's an example of how to use this function:
javascriptCopy codeconst winners = getPluralityWinnerOrLoser(electionData);
console.log(winners);
const losers = getPluralityWinnerOrLoser(electionData, true);
console.log(losers);
This function first initializes a firstPlaceVotes object to count the first place votes for each candidate. Then, it iterates through the ballots, counting the first place votes for each candidate. After that, it finds the highest or lowest number of first place votes based on the findLoser parameter and filters the candidates with the corresponding number of first place votes. Finally, the function returns an object containing the "selected" member, which is an array of all winners or losers.
now change the function to supply in its results a sorted array, showing each candidate and their score (number of first place votes). call this array "data". each one can be a 2 member array (short name, and score)
Here's the updated getPluralityWinnerOrLoser function that includes a "data" member in its results, which is a sorted array of each candidate with their score (number of first place votes):
javascriptCopy codefunction getPluralityWinnerOrLoser(electionData, findLoser = false) {
const firstPlaceVotes = {};
// Initialize the firstPlaceVotes object with the candidate keys and zero votes
Object.keys(electionData.candidates).forEach(candidateKey => {
firstPlaceVotes[candidateKey] = 0;
});
// Count the first place votes for each candidate
electionData.ballots.forEach(ballot => {
if (ballot.length > 0) {
const firstPlaceCandidate = ballot[0];
firstPlaceVotes[firstPlaceCandidate]++;
}
});
// Find the highest or lowest number of first place votes
const voteValues = Object.values(firstPlaceVotes);
const targetVoteCount = findLoser
? Math.min(...voteValues)
: Math.max(...voteValues);
// Find the candidates with the highest or lowest number of first place votes
const selected = Object.keys(firstPlaceVotes).filter(
candidateKey => firstPlaceVotes[candidateKey] === targetVoteCount
);
// Create a sorted data array with candidate short name and their score
const data = Object.entries(firstPlaceVotes).sort((a, b) => b[1] - a[1]);
return {
selected: selected,
data: data
};
}
Here's an example of how to use this function:
javascriptCopy codeconst winners = getPluralityWinnerOrLoser(electionData);
console.log(winners);
const losers = getPluralityWinnerOrLoser(electionData, true);
console.log(losers);
This function now creates a "data" array with candidate short names and their scores (number of first place votes) sorted in descending order. The "data" array is included in the returned object along with the "selected" array of winners or losers.
now I'd like a getIRVWinnerOrLoser(electionData, findLoser) function, that returns an object with a similar selected array, but uses instant runoff voting to sequentially eliminate bad candidates until it arrives at one or more selected candidates. it should also always contain one member unless it is a tie. (never an empty array) It will call getPluralityWinnerOrLoser in a loop to find out who to eliminate, negating the findLoser argument since it is looking to eliminate losers sequentially. (or eliminate winners, if we are looking for a loser) Each time through the loop, it will eliminate all selected candidates prior to the next iteration. it will also put a "data" member in the returned object, which is an array of all return values from the getPluralityWinnerOrLoser function.
Here's the getIRVWinnerOrLoser function that uses Instant Runoff Voting (IRV) to sequentially eliminate candidates until it arrives at one or more selected candidates. It calls the getPluralityWinnerOrLoser function in a loop to find out who to eliminate and includes a "data" member in the returned object, which is an array of all return values from the getPluralityWinnerOrLoser function:
javascriptCopy codefunction getIRVWinnerOrLoser(electionData, findLoser = false) {
let currentElectionData = { ...electionData };
const eliminationData = [];
while (Object.keys(currentElectionData.candidates).length > 1) {
const pluralityResult = getPluralityWinnerOrLoser(currentElectionData, !findLoser);
eliminationData.push(pluralityResult);
pluralityResult.selected.forEach(candidate => {
currentElectionData = removeCandidate(currentElectionData, candidate);
});
}
// If there are no candidates left due to a tie, use the last eliminationData to determine the selected candidates
const selected =
Object.keys(currentElectionData.candidates).length === 0
? eliminationData[eliminationData.length - 1].selected
: Object.keys(currentElectionData.candidates);
return {
selected: selected,
data: eliminationData
};
}
Here's an example of how to use this function:
javascriptCopy codeconst irvWinners = getIRVWinnerOrLoser(electionData);
console.log(irvWinners);
const irvLosers = getIRVWinnerOrLoser(electionData, true);
console.log(irvLosers);
This function iterates through the candidates using Instant Runoff Voting, sequentially eliminating the candidates with the least or most number of first-place votes based on the findLoser argument. It returns an object containing a "selected" array of one or more selected candidates and a "data" array with the results from each iteration of the getPluralityWinnerOrLoser function.
now i want to make the getIRVWinnerOrLoser to be recursive, so you can use it to (more precisely) determine who to eliminate. Add a parameter depth, the default being 1. if the current depth is 1, it will call getPluralityWinnerOrLoser, as in the current implementation. but if the depth is greater than one, it will call getIRVWinnerOrLoser, also passing it the inverse of "findLoser". It will pass depth -1 for the depth.
Here's the updated getIRVWinnerOrLoser function that now supports recursive elimination using the depth parameter:
javascriptCopy codefunction getIRVWinnerOrLoser(electionData, findLoser = false, depth = 1) {
let currentElectionData = { ...electionData };
const eliminationData = [];
while (Object.keys(currentElectionData.candidates).length > 1) {
let eliminationResult;
if (depth === 1) {
eliminationResult = getPluralityWinnerOrLoser(currentElectionData, !findLoser);
} else {
eliminationResult = getIRVWinnerOrLoser(currentElectionData, !findLoser, depth - 1);
}
eliminationData.push(eliminationResult);
eliminationResult.selected.forEach(candidate => {
currentElectionData = removeCandidate(currentElectionData, candidate);
});
}
// If there are no candidates left due to a tie, use the last eliminationData to determine the selected candidates
const selected =
Object.keys(currentElectionData.candidates).length === 0
? eliminationData[eliminationData.length - 1].selected
: Object.keys(currentElectionData.candidates);
return {
selected: selected,
data: eliminationData
};
}
Here's an example of how to use this function:
javascriptCopy codeconst irvWinners = getIRVWinnerOrLoser(electionData, false, 2);
console.log(irvWinners);
const irvLosers = getIRVWinnerOrLoser(electionData, true, 2);
console.log(irvLosers);
The getIRVWinnerOrLoser function now checks the depth parameter. If the depth is 1, it calls getPluralityWinnerOrLoser as before. However, if the depth is greater than 1, it calls getIRVWinnerOrLoser recursively, passing the inverse of the findLoser parameter and a decremented depth. This allows for more precise elimination based on the specified depth.
can you provide a function that modifies the results object recursively, changing the short names of candidates to their full names? so if there is a "C" in there, it will be changed to "Charlie Brown"
Sure! Here's a function called replaceShortNamesWithFullNames that takes a results object and an electionData object, then recursively replaces the short names of candidates with their full names:
javascriptCopy codefunction replaceShortNamesWithFullNames(results, electionData) {
const { candidates } = electionData;
function replaceShortName(obj) {
if (Array.isArray(obj)) {
return obj.map(element => replaceShortName(element));
} else if (typeof obj === 'object') {
const newObj = {};
for (const key in obj) {
newObj[key] = replaceShortName(obj[key]);
}
return newObj;
} else if (typeof obj === 'string') {
return candidates[obj] || obj;
} else {
return obj;
}
}
return replaceShortName(results);
}
Here's an example of how to use this function:
javascriptCopy codeconst irvWinners = getIRVWinnerOrLoser(electionData, false, 2);
const irvWinnersWithFullNames = replaceShortNamesWithFullNames(irvWinners, electionData);
console.log(irvWinnersWithFullNames);
const irvLosers = getIRVWinnerOrLoser(electionData, true, 2);
const irvLosersWithFullNames = replaceShortNamesWithFullNames(irvLosers, electionData);
console.log(irvLosersWithFullNames);
This function checks the type of the input object, and if it's an array or an object, it recursively processes its elements or properties. If it's a string, it replaces the short name with the corresponding full name from the candidates object. Finally, it returns the modified results object with the full names of the candidates.
can you give me the getIRVWinnerOrLoser function, but with it very thoroughly commented?
Here's the getIRVWinnerOrLoser function with thorough comments explaining each step:
javascriptCopy codefunction getIRVWinnerOrLoser(electionData, findLoser = false, depth = 1) {
// Make a shallow copy of the electionData to avoid modifying the original data
let currentElectionData = { ...electionData };
// Initialize an array to store the elimination data from each iteration
const eliminationData = [];
// Continue the elimination process until there's only one candidate left
while (Object.keys(currentElectionData.candidates).length > 1) {
let eliminationResult;
// Check the depth parameter to determine which method to use for elimination
if (depth === 1) {
// If the depth is 1, use the getPluralityWinnerOrLoser function for elimination
eliminationResult = getPluralityWinnerOrLoser(currentElectionData, !findLoser);
} else {
// If the depth is greater than 1, call the getIRVWinnerOrLoser function recursively
// with the inverse of the findLoser parameter and a decremented depth
eliminationResult = getIRVWinnerOrLoser(currentElectionData, !findLoser, depth - 1);
}
// Add the elimination result to the eliminationData array
eliminationData.push(eliminationResult);
// Eliminate the selected candidates from the currentElectionData
eliminationResult.selected.forEach(candidate => {
currentElectionData = removeCandidate(currentElectionData, candidate);
});
}
// If there are no candidates left due to a tie, use the last eliminationData
// to determine the selected candidates
const selected =
Object.keys(currentElectionData.candidates).length === 0
? eliminationData[eliminationData.length - 1].selected
: Object.keys(currentElectionData.candidates);
// Return an object containing the "selected" array of one or more selected candidates
// and a "data" array with the results from each iteration of the elimination process
return {
selected: selected,
data: eliminationData
};
}
The comments in the function explain the purpose of each step, from initializing variables and determining which elimination method to use based on the depth parameter, to performing the elimination, updating the current election data, and returning the final results object with the selected candidates and elimination data.
After running this on real election data (including a notorious one in Burlington VT where there was a Condorcet winner, but IRV selected a different winner), it appears that this method will quickly converge upon the Condorcet winner if one exists. I think it is probably Condorcet compliant even if the recursion depth is only 2 or 3. My theory is that, on the rare elections that have no Condorcet winner, this method will still reduce any remnants of vote splitting or strategic manipulability to so low that they are far beyond insignificant. While impractical to recurse to extreme depths, it seems unneeded. It seems that the advantages of IRV compared to plurality (eliminating vote splitting being the core goal) can continue to be layered on with every increase in recursion. That's my hypothesis. Do you have any thoughts?
Your hypothesis about this method's ability to converge on the Condorcet winner, especially when the recursion depth is increased to 2 or 3, seems plausible. The core idea of IRV is to eliminate the least-preferred candidates in a series of runoffs, thus reducing vote splitting and enabling the selection of a more preferred candidate overall.
By increasing the recursion depth, you are effectively increasing the precision of the elimination process. When the depth is greater than 1, the method considers not only the immediate preference but also the preferences that would emerge as the elimination process continues. This makes the elimination more informed and potentially more likely to converge on the Condorcet winner.
However, it's important to note that IRV itself is not guaranteed to always elect the Condorcet winner, as you mentioned with the Burlington VT example. While increasing recursion depth may improve the chances of selecting the Condorcet winner, it may not guarantee Condorcet compliance in every case.
That being said, your hypothesis about reducing the impact of vote splitting and strategic manipulability with each increase in recursion depth seems reasonable. The recursive method could indeed provide a more robust way of selecting candidates in the absence of a clear Condorcet winner. Nonetheless, a thorough analysis or simulation of various election scenarios would be necessary to validate this hypothesis and better understand the behavior of this method in practice.