2225: Voting Referendum

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Voting Referendum
The weirdest quirk of the Borda count is that Jean-Charles de Borda automatically gets one point; luckily this has no consequences except in cases of extremely low turnout.
Title text: The weirdest quirk of the Borda count is that Jean-Charles de Borda automatically gets one point; luckily this has no consequences except in cases of extremely low turnout.


Ambox notice.png This explanation may be incomplete or incorrect: Created by a VOTING SYSTEM. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.
If you can address this issue, please edit the page! Thanks.

The main part of this comic is a ballot on the subject of voting methods—that is, of ways to choose one or more winning options from a set of options at an election.

The first three options are shown with radio buttons, a standard ccomputer convention for a choice where the user may make only one selection, and they are indeed methods where a voter selects one and only one option.

The first listed, first-past-the-post, is a common method used in the USA, UK, and Canada where an election will select only one winner. Each voter selects one preferred candidate, and the one with the most votes wins, even if that is a small fraction of the total (the winner of the UK Parliamentary seat for Belfast South in 2015 did not even receive a quarter of the vote).

The second listed, the top-two primary, is the system used in California for USA House of Representatives elections. Candidates from all parties and from no party all appear on one ballot at the primary (unlike most states, where each party’s primary is a separate race, winners then proceeding to the first-past-the-post general election). The two highest finishers then contest the general election, even if both are from the same party, and even if one had an absolute majority in the primary. (This is because the Constitution requires that representatives be elected on the same day, and having a seat decided in advance via the primary would violate this.)

The third, the Louisiana primary, is more like the traditional runoff system, in that the second part of the election is not held if one candidate has a clear majority (one vote more than the combined total of all other candidates). In this case, though, the primary is held on the national Election Day, and any needed runoffs are held on a later date. This also resembles the system used in France, where the runoff is known as the "deuxième tour" (the "premier tour" being the main election).

The next option is cumulative voting, in which each voter gets as many votes as there are seats to be filled, and may distribute them as he chooses among one or more candidates. This system was long used to select the Illinois House of Representatives; its most common use today is in choosing corporate boards of directors. A computer would typically represent this kind of choice with multiple columns of radio buttons (one per vote), each candidate represented by one row (as we see here).

The next two methods involve voting yes or no on each option presented, which the comic represents with the traditional metaphor of a checkbox.

Approval voting is the single-winner version of this system, in which the most-approved-of candidate is the winner. This system is not in widespread use, but was adopted in 2018 in Fargo, ND, USA.

Under multiple non-transferable vote, a voter may vote for up to k candidates (in a k-winner election), and the k highest vote-getters win. This system resembles cumulative voting, but without the ability to concentrate votes on candidates. Its use in the USA has been largely outlawed because it allows a cohesive majority of voters to claim all of the seats and thus to deny the minority any representation whatsoever.

The next three methods involve allowing voters to rank their preferred alternatives from best to worst, represented by numeric entry fields.

The simplest of these, instant runoff voting, is increasingly popular for single-winner elections. The conventional runoff (in which the top candidates run again if there is no clear majority), as described above, requires holding a second election, printing new ballots, renting the voting spaces, and otherwise incurring additional cost. Under the instant-runoff system, voters indicate their lower preferences on the same ballot as their main vote, and the runoff election is "held" by using this data.

The single transferable vote system extends this concept to multiple-winner elections. A candidate wins by reaching a vote total of (v/(k+1))+1, or just enough to prevent there from being too many winners. Excess votes for a winner are then distributed to those voters’ next choices, as are those cast for the bottom candidates eliminated when no additional winners can otherwise be determined. The Republic of Ireland elects its lower house, the Dáil, by this system.

Under the Borda count system, each ballot is counted as 1 points for the last choice, 2 for next-to-last, and so on up to n for the first choice among n candidates. The highest point-earner(s) win)s(. This system may also be calculated as 1 point for first choice, 2 for second, etc., with the lowest total winning; this variant, called the "cross-country vote" (due to its resemblance to the scoring system of the sport of cross-country running), is used by the National Collegiate Athletic Association’s various selection committee as one step in choosing championship tournament fields.

Finally, range voting allows a voter to give any value in a range (say 0 to 10) to each candidate, with the highest total winning. (If the range contains only two values, this reduces to the approval system.) Our imaginary voter is asked to choose the point on the range by way of a slider, the classic computer metaphor for it.

The punchline is that the whole referendum is a chicken-and-egg problem: in order to accomplish the purpose of a referendum, one needs to know how the votes will be translated into a result, but in this case, determining that rule is the purpose of the referendum....

The alt text refers to the inventor of the Borda count (for whom it is named), implying that the use of the system includes a ballot in which he gets one vote. This vote would be quickly drowned out by any sensible quantity of actual votes.

The day before this comic's publication was an election day throughout the USA, primarily for local and state issues (normal elections for federal offices of the President, Senate, and House of Representatives are always in even years), so the topic of today's comic highlights many different methods for conducting elections and counting votes. While elections are primarily used to allow voters to select from candidates for public offices, election ballots also frequently present questions for voters to directly voice their support or opposition to some change in a process or law - commonly called a referendum. The comic depicts an election ballot referendum for voters to select the method to be used in future elections.

  • First past the post

The aim of political elections is to determine which of the candidates standing for election is favoured by the majority of voters. In a simple two person contest, this process is trivial, since whichever candidate receives the most votes will be the one that the majority of voters prefer. This First-past-the-post_voting system works well for simple cases, but for elections with more than two candidates this system may result in a candidate being elected who less than 50% of the voters would prefer.

For example, in a contest with three candidates; A, B and C, where candidate A received 41% of the vote, candidate B 40% and candidate C 19%, then candidate A will be elected, even though some of the voters who chose candidate C might have preferred candidate B as their second choice instead of candidate A, leading to a result which pleases fewer than half of the population.

Despite this drawback, First Past the Post voting continues to be used for political elections in many countries including the US and UK, which historically have both had two main parties receiving the majority of votes. The First Past the Post system has received much criticism, particularly from smaller parties who may loose out, however supporters promote the simplicity of the system compared to other methods.

  • Top-two primary

  • Louisiana primary

  • Cumulative voting

  • Approval voting

In this system, each candidate is listed as a yes/no choice, where the voters can choose which candidate they approve of winning the election, and which ones they do not approve of. The winner of the election is the candidate with the highest approval rate.

In the XKCD ballot, the approval option is presented as a checkbox, where a check in the box is "approve" or an empty box is "disapprove".

  • Multiple non-transferable vote

  • Instant runoff voting

In this system, people vote for all the candidates, or perhaps their favorite three, but assign different preferences to each candidate they vote for, as in 1 for their first choice, 2 for the second, 3 for their third, etc. If enough people vote for a candidate as their first choice to clear 50%, that person wins. If not, the person with the least votes gets eliminated, and anyone who voted for that person has their next (slightly less favorable) choice automatically move up a rung. The 50% mark is again checked, and if no winner another lowest-voted candidate is eliminated. Eventually one candidate will emerge victorious, and overall that person will have been liked by the voters more than anyone else. The advantages of this system are there is rarely a need to have another election if things are close (the information is already there to "instantly" recalculate the vote based on additional voter preferences), and there is no concept of a "spoiler" candidate taking votes away from your favorite. If people are truly voting their favorite, second favorite, etc., no vote need be seen as being thrown away. For example, a voter really likes the Hippo candidate even though few others do. They can still vote that candidate #1 and the apparently-popular Giraffe candidate 2nd, knowing that if Hippo is eliminated, they have still voted for Giraffe and that vote counts. If it turns out people secretly really like Hippo, however, that candidate actually has a real chance because people are not trying to guess what candidate everyone else will vote for in order to ensure Vulture doesn't get in.

On this weird XKCD ballot, we see this type of ranking between this type of voting (Instant runoff voting) and the two that follow (Single transferable vote and Borda count).

  • Single transferable vote

In the

  • Borda count


Voting Referendum

Which voting system should we use?

  • (empty radio button) First past the post
  • (empty radio button) Top-two primary
  • (filled radio button) Louisiana primary
  • (two filled, one empty radio button) Cumulative voting
  • (checked box) Approval voting
  • (checked box) Multiple non-transferrable vote
  • (box marked "3") Instant runoff voting
  • (box marked "1") Single transferrable vote
  • (box marked "2") Borda count
  • (slider with value slightly below half) Range voting

The referendum went well, but we can't figure out how to count the ballots.

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OK, I just created a massive edit conflict, I see. Will move my content into the appropriate parts of the template already in place. Silverpie (talk) 20:37, 6 November 2019 (UTC)

If there is disagreement about which edits are better, we should vote on it. Which system of voting would be best for that? -boB (talk) 21:08, 6 November 2019 (UTC)

Someone (IP-User) just added the following:

Additionally, in election of multiple candidates across a country (or region etc.), first past the post does not lead to a distribution of elected representatives proportional to the total number of votes, only electing the lead candidate in each case. For example, imagine a country with 100 representatives to be elected, with each seat having the same distribution as described in the example above. Under first past the post, 100 representatives will be elected representing part A, and none for party B or C.

Unless there is some example where this is used (multiple seats given only to the winner of a first past the post) I'd vote for removing this statement. As I do not know all (or even many) democratic systems worldwide, I am not sure if it might be relevant somewhere. --Lupo (talk) 13:58, 7 November 2019 (UTC)

That's how the US Electoral College works: in each state, all elector seats go to the party that obtained the majority of votes. 14:53, 7 November 2019 (UTC)
Really? I knew that the "electoral college" was fucked up, but I was not aware, that the US system is this bad... --Lupo (talk) 15:06, 7 November 2019 (UTC)
The US system is the most broken system in a democracy... See CGP Greys videos on first past the post and general playlist of Politics in America. --Kynde (talk) 21:05, 7 November 2019 (UTC)
Sort of – that's how most states choose to allocate their electors (who don't actually *have* to vote for the candidate they're pledged to, but that's a whole other story). Some states, like Maine, do it proportionally instead. See the wikipedia section on alternative methods of choosing electors. BobbingPebble (talk) 14:27, 9 November 2019 (UTC)

Problem of selecting the method of voting was already considered in Polish comedy The Cruise (Pol. Rejs). "But what voting system can be used to select the method of voting?" Tkopec (talk) 09:34, 8 November 2019 (UTC)

Also a BBC Radio sketch show (whose title escapes me right now, sorry) had a whole skit about (randomly) choosing something by going through all kinds of 'decision' methods with a sequence featuring things like "...but who rolls the dice?" / "We'll flip a coin for it" / "But whose coin do we flip?" / "We'll draw lots for it." / "But who draws first..?" with it wrapping round back to the first undecidable decision-method. But written better, naturally... ;) 19:06, 11 November 2019 (UTC)
Louisiana Primary

I didn't know - WikiP: The so-called Louisiana primary is the common term for the Louisiana general election for local, state, and congressional offices.[1] On election day, all candidates for the same office appear together on the ballot, often including several candidates from each major party. The candidate who receives a simple majority is elected. If no candidate wins a simple majority in the first round, there is a runoff one month later between the top two candidates to determine the winner. This system is also used for United States Senate special elections in Mississippi and Texas, and all special elections for partisan offices in Georgia.[2]Afbach (talk)

This is also known as a "Jungle Primary" and is also done in Washington state and California. 20:00, 6 November 2019 (UTC)

I had to resolve an editing conflict in the first paragraph with another editor, but please feel free to further resolve our differing edits. Ianrbibtitlht (talk) 20:26, 6 November 2019 (UTC)

Single Transferable Vote

The text says "100%/(k+1)". Surely this should be "100%/k + 1", or "100%/k, plus one person"? Say k is 4. The current text implies that only 20% is required, when it should be 25%, plus one person. John.Adriaan (talk) 01:55, 7 November 2019 (UTC)

Setting a quota at 25% plus one person would only allow 3 people to be elected, as once that happens there would be less than 25% of the vote left to count which wouldn't be enough to elect anyone else. Setting the quota at 100%/(k+1) means that k people can be elected before the remaining vote isn't enough to elect anyone else (setting the quota at exactly 100%/k, by the way, has also been used and is known as the Hare quota). Arcorann (talk) 02:21, 7 November 2019 (UTC)
Say k is 4. Then 100%/(4+1) = 20%. So, yes, it's possible that you could end up with 5 people all getting exactly 20%. But a perfect 5-way tie like that would be extremely unlikely. Other than that very improbable result, only 4 people could get elected, as is desired. Imagine, for example, one person gets juuust over 20% of the vote. Even just that little bit over means there's less than 80% of the vote left for the other four. Which means only 3 of the remaining 4 people could get over the 20% threshold.
Of course the correct formula should be "100%/(k+1)+1". -- Hkmaly (talk) 04:23, 7 November 2019 (UTC)
Which could result in no-one being elected if, say, 5 candidates each get exactly 20% of the vote. 22:17, 7 November 2019 (UTC)
Which would be in some sense fair, as noone is more favourable to the voters than the other 4 candidates, while there is only 4 seats... So there needs to be a second referendum or some other measure for that case. --Lupo (talk) 06:59, 8 November 2019 (UTC)
In that case the system would handle the situation the same way it handles ties when candidates have smaller numbers of votes (every system needs to handle ties somehow, after all). Arcorann (talk) 09:23, 8 November 2019 (UTC)

I just came here to see if there was a discussion on which system actually should be selected, according to the ballot displayed. I'm sadly disappointed that there isn't one, lol. 17:25, 7 November 2019 (UTC) Sam @Sam, just for you then: According to the ballot displayed, I, as the Commissioner of XKCD Voting Comic voting, and retired OTTer, hereby remind you that it isn't what people vote for but who counts the votes. I've counted, and the winning system is [redacted] Cellocgw (talk) 15:22, 8 November 2019 (UTC)

Can we hold an election for who gets to give me all their money, use the Borda count, and then not vote at all? So he'd pay me (if he's still alive of course). SilverMagpie (talk) 20:16, 8 November 2019 (UTC)

Assume that counting votes under the best election method will select the best election method. IOW, the best election method will select itself. So, if there happens to be exactly one election method that chooses itself, then the problem is solved. 02:09, 9 November 2019 (UTC)

TIL that I independently reinvented the Borda count method. One way that I use it is in a spreadsheet that ranks my cards in the Animation Throwdown online card game. I hope that Borda's heirs aren't royalty-happy. These Are Not The Comments You Are Looking For (talk) 20:48, 10 November 2019 (UTC)

With FPTP, which was the obvious go-to-method, we always elected a boy as class-speaker, even though we had more girls in our class, back in school. While there was usually just one boy interested, who got himself up as a candidate, he got all of the boys votes, while the girls votes where usually split across 2 or 3 female candidates they fielded. So even though the girls were more engaged in school-politics, they never provided the class speaker... --Lupo (talk) 15:41, 13 November 2019 (UTC)

I know nobody has commented on this article for over 2⅓ years, but I was reading the explanation just now for the "First past the post" section, and something in it bothers me. It says "For example, [if] ... A receives 43%, ... B 38%, and ... C 19%, candidate A will be elected" and then later says "the above distribution of votes happened in the 2000 United States presidential election in Florida..." So... did it used to actually have the voting percentage distributions for Bush, Gore, and Nader (which would be, respectively, 48.85%, 48.84%, and 1.64% of total votes cast - with an additional 0.68% voting for others - or, alternatively (but less straightforward), out of all the votes cast for those three, 49.18%, 49.17%, and 1.65%) Mathmannix (talk) 19:27, 23 March 2022 (UTC)