2225: Voting Referendum
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.
The day before this comic's publication was an election day throughout the United States, primarily for local and state issues (normal elections for federal offices of the President, Senate, and House of Representatives are always in even years). 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. While the referendum is asking voters to select a method from a long list of methods, a referendum is usually presented as a specific proposal which requires a simple Yes or No vote.
As an example, the ballot in New York City included a referendum (which passed) on whether to use a different method, ranked choice voting (another name for instant-runoff voting as described below).
A common issue with such referenda is what method to use to conduct the referendum itself. Here, the method of marking each choice on the ballot reflects the marking method which would be used if it were the winner. Moreover, each item is listed in a way which is suggestive of what it means (e.g., "First past the post" is the first one, "Top-two" is among the top two, and "Multiple non-transferable vote" is selected among numerous other ones). A few of the methods allow for multiple winners, which can often be good when electing councils and representatives, but it is unclear what it would mean to have several of these voting methods all win.
The aim of political elections in first-past-the-post is to determine which of the candidates standing for election is most preferred by the most voters. In a simple two-person contest, this process is quite effective, since whichever candidate receives the most votes will be the one that the majority of voters prefer. This 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, in which candidate A receives 43% of the vote, candidate B 38%, and candidate C 19%, 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 less than half of the population. For example, the above distribution of votes happened in the 2000 United States presidential election in Florida, where George W. Bush beat Al Gore by less than 1000 votes largely because of the third-party candidacy Ralph Nader, whose 100,000 voters would mostly have otherwise gone to Gore.
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 party A, and none for party B or C.
Despite these drawbacks, 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 lose out; however, supporters promote the simplicity of the system compared to other methods.
This system is shown with a radio button, the classic computer metaphor for being allowed one choice out of a set.
This method is used in California and Washington to select candidates for the US House of Representatives. In most states' primary-election systems, each party votes separately to select one candidate to continue to a first-past-the-post general election ballot. In these two states, on the other hand, candidates from all parties, as well as "independent" candidates from no party, run in a single race, and the top two finishers then contest the general election, even if both are from the same party (a common occurrence in heavily-Democratic California), and even if one candidate has a clear majority of the vote. (In an older version, a majority winner in the primary was immediately declared elected. This was held to be in violation of federal law, by effectively setting an "election day" before the national Election Day in November.)
This system is almost identical to the top-two primary, but with two differences. First, the open-to-all ballot is held on the national Election Day, instead of on the state's primary day. (This avoids the conflict with Federal law described above.) Also, the second round of the election is not held if one candidate has a clear majority (more than 50%) of the votes in the first round. Like the top-two primary and the first-past-the post system, the comic represents this system with a radio button, except this one has been marked, indicating the vote.
In cumulative voting, each voter gets as many votes as there are seats to be filled, and may distribute them as he chooses. This system's most common use is in selecting corporate boards of directors. It is also used in some areas to allow a minority bloc within an electorate to elect some of its preferred candidates without imposing a system of separate districts.
The comic illustrates this with multiple radio buttons, each row representing an option/candidate and each (implied) column one vote. On the ballot the first 2 radio buttons are marked, as they are each the only radio buttons in their column and cannot be unmarked..
In this system, each candidate is listed as a yes/no choice, where the voters can choose which candidates 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.
This type of voting system can be used as a vetting process to filter out undesirable candidates before the final vote; for example, the United Nations uses a series of "straw polls" to filter out candidates for the Secretary General before the Security Council makes a final vote. In 2018, Fargo, North Dakota switched to using approval voting to elect local politicians, making it the only jurisdiction in the United States to use this system. 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". Checkboxes are distinct from radio buttons in that several can be marked in the same field, and can also be unmarked without marking another.
This system for electing multiple members to a ruling body is also known as plurality-at-large voting or block vote. It is commonly used in the US for city council elections, and simply limits the number of votes per voter to the number of winners. It allows a cohesive plurality of the electorate to claim all of the seats, denying other voters any representation whatsoever.
In 2019, the Justice Department required Eastpointe, Michigan to run at least the next two elections via single transferable vote because their existing plurality-at-large system was disenfranchising black citizens.
This system is also shown as a checkbox, as each candidate gets either 0 or 1 votes from each voter.
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 at least 50% of voters vote for a candidate as their first choice, that candidate 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 there is no winner, another lowest-voted candidate is eliminated. Eventually one candidate will emerge victorious. The advantages of this system are that 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 "spoiler" candidates only cause problems when they become competitive. And as Arrow's impossibility theorem shows, as with all ranking methods, sometimes voters can hurt a candidate by ranking them more favorably.
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), all of which allow multiple ranked votes. It appears that between these three, Randall has voted for Single transferable vote as his top choice, Borda count for his second choice, with Instant runoff voting as his third choice.
This system extends the instant runoff to multiple-winner elections. Specifically, the election threshold is set not at 50%, but at 100%/(k+1) where k candidates will win (in other words, just high enough to prevent more candidates from reaching it than there are seats). The bottom candidates are eliminated as in instant-runoff and their votes redistributed. In addition, if a candidate wins with more than enough votes, the extra votes (either a fraction of each vote, or some subset of the ballots) are also redistributed. This procedure continues until the requisite number of winners is reached.
Each ballot is counted as 1 point 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. 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 NCAA's various selection committee as one step in choosing championship tournament fields.
The title text refers to the inventor of the Borda count, Jean-Charles de Borda (for whom it is named), implying that the use of the system implies the inclusion of a ballot in which he gets one point in the counting. This "1 point" would be quickly drowned out by any sensible quantity of actual votes. This also humorously suggests that if no one were to vote at all, Borda would win by default.
For each candidate, the voter selects a value within a fixed range (the xkcd voter sees this choice presented as a slider) for each candidate, independent of the values given to other candidates. The highest total wins. (If the range is restricted to two values, this becomes the approval system.)
The punchline for the comic 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. Additionally this xkcd demonstrates one of the mechanisms that makes it hard to change the currently-used voting system in any state: Each voting system in fact votes for itself as the ones who are able to decide upon the voting system being in use have been elected using the current voting system and therefore are likely to profit from it.
- [A voting ballot is shown with an underlined header and 10 different options below with different boxes/buttons next to each choice. Some are empty, some are marked/checked or numbered.]
- Which voting system should we use?
- [Empty radio button]: First past the post
- [Empty radio button]: Top-two primary
- [Filled radio button]: Louisiana primary
- [Three radio buttons in a row, first two filled]: 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
- [Caption below the panel:]
- The referendum went well, but we can't figure out how to count the ballots.
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