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I'd like to explore the development of a country that has a political system where people vote for their favourite candidate and against their least favourite. The against votes are subtracted from the for votes. This could mean that some people would get negative votes - the least negative would win.

My instinct tells me that this measure would make for fairer voting. Am I blind to the disadvantages? Are there any drawbacks that I'm missing?


Assumption

This takes place in a Western democracy (such as the UK), the only difference being the voting system.

Please ask if anything is not clear

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    $\begingroup$ This would also be on-topic for politics SE, and I have seen many similar questions there. $\endgroup$ May 9 at 14:12
  • $\begingroup$ I don't know if you would consider this as a drawback, but this would surely favour more consensual candidates and make politicians even more risk-averse than they are now, about virtually anything. $\endgroup$
    – Jivan
    May 9 at 21:48
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    $\begingroup$ @OmarL, looks quite typical to me. Parliamentary monarchy is used in Canada, and many European countries. $\endgroup$
    – lvella
    May 10 at 13:03
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    $\begingroup$ Could be studies by game theory, and ought to be ... My intuition is that this would be even more random than many voting systems used today! Neither does it sound very democratic to hinder other people choosing their representatives, as this would be. It would also increase scope for strategic/tactical voting. $\endgroup$ May 10 at 15:38
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    $\begingroup$ Cancel culture... $\endgroup$
    – Anixx
    May 16 at 9:39
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We already have something very similar to that which has been proven to work: Ranked Choice Voting. Everyone chooses their candidates in order from most preferred to least preferred. In this system, the number of offices to be voted divided by the number of voters sets a threshold minimum. All rank 1 votes are tallied, if all top candidates meet the threshold, they win. If not, the lowest candidate is eliminated and the rank 2 votes from those voters are added to the remaining candidates. This repeats until all top candidates meet the threshold.

The problem with the simple choose one to +1, and one to -1, is that it's likely that a minority winner will be selected, so the fewest number of people are likely to be represented. This would likely happen because the "least hated" person would win, rather than the "generally most liked" person winning.

Consider a thousand votes:

Candidate Votes For Votes Against Result
Alice 501 499 2
Bob 3 0 3
Charlie 496 501 -5

Nobody particularly wanted Bob, but nobody didn't want Bob, so he wins even though only 0.3% of the population voted for him. Maybe he didn't campaign at all, and the only three people who voted for him were his parents and a close friend. He'd actually end up winning from a lack of information about his policies, character, etc. Or maybe he didn't actually put any policies out, only negative campaigns against his opponents. It's likely that the "negative ads" that we see in the real world would be even more pronounced; they'd want to end up being the least hated person for the best chance of winning.

This could be an interesting plot device where nothing ever seems to get done because the only people who end up getting voted in are those that have never held office and remained relatively unknown, perhaps even cycles of greater and greater political disasters because the unknowns keep winning; the last person in office did a terrible job, becoming the most hated, allowing the newest least hated person to win.

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    $\begingroup$ "This could be an interesting plot device" +1. Sounds like a great reason to go with this for a story! 😃 BTW, does ranked choice avoid this problem? $\endgroup$
    – Matthew
    May 9 at 15:02
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    $\begingroup$ @Matthew Yes, it avoids the problem by having choosing the candidates that are preferred by most voters, rather than choosing the "least hated" option. $\endgroup$
    – phyrfox
    May 9 at 15:11
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    $\begingroup$ Good answer. I'd vote for Bob! $\endgroup$ May 9 at 15:48
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    $\begingroup$ This seems to be answers from an American style system, just 3 parties. Here in the Netherlands we have multiple parties (10+) from which you can choose. You can +1 your own party and -1 the more (very) right parties. A lot of people arent the biggest fan of a normal other party, but often very much dislike the (very) right ones. So it likely wont be so close to eachother as a 3 options system would $\endgroup$
    – Martijn
    May 10 at 7:41
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    $\begingroup$ I think within the context of that system, selecting a candidate that is "least hated" amongst the popular choices is the point rather than a problem... the equivalent problem with the "normal" system is when there are a large field of candidates, with one that most people hate with a passion, but whose supporters are larger in number than those for any single other candidate, so the current system supports a highly divisive candidate who (even with some degree of tactical voting) is merely hated by fewer people than the other option. $\endgroup$
    – Steve
    May 10 at 7:56
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This is how Australian voting effectively works in practice.

Australia is officially "Ranked choice voting" - You order N candidates from 1 to N, however I can tell you from experience and anecdotally that Australians typically vote "for" and "against" first, and then fill in the blanks between.

So for example, my recent voting slip looked something like this:

  • _ _ _ Centre left party | Mr Cleft
  • _ _ _ Centre right party | Mr Cright
  • _ _ _ Environment / mid left party | Mrs Green
  • _ _ _ Christian right party | Fr Right
  • _ _ _ Super right xenophobic party | Mr Hitler

I approached this ballot paper, immediately decided that I was voting "For" Mrs Green, and "Against" Mr Hitler. So my ballot paper looked like:

  • _ _ _ Centre left party | Mr Cleft
  • _ _ _ Centre right party | Mr Cright
  • _ 1 _ Environment / mid left party | Mrs Green
  • _ _ _ Christian right party | Fr Right
  • _ 5 _ Super right xenophobic party | Mr Hitler

I then filled in the blanks - in rough political spectrum order:

  • _ 2 _ Centre left party | Mr Cleft
  • _ 3 _ Centre right party | Mr Cright
  • _ 1 _ Environment / mid left party | Mrs Green
  • _ 4 _ Christian right party | Fr Right
  • _ 5 _ Super right xenophobic party | Mr Hitler

I voted "for" and "against" two separate parties. I could also vote entirely "for" a party (put a 1 there and then copy in their "how to vote card" which their party volunteers are usually holding by the entrance gate) or entirely "against" a party (put them last and then fill every other box with random noise - or copy in their how to vote card with the numbers reversed)

The end result implements the behaviour you want: A vote "against" a party will flow through all their opponents in the system in priority order - it will always stay against my 5th preference for the entire vote tally (moving through 4 candidates in order) thus increasing the vote count required by Mr Hitler in order to win by 1. The same effect as voting "-1" to him.

And this example only had 5 so was kind of trivial (we'd get this for our lower house elections). Our upper house you're looking at numbering typically 60. Many just put in the 1 and call it done (trusting their #1 party to direct their preferences), but I want to explicitly put the crazy parties last, so I put a 1 for my favourite party, and I put a 60 for the craziest, fill up the 50s with the hard NOs, and then I work towards the middle.

This fixes the issue Phyrfox identified and ensure the plurality gets their way:

(Democracy isn't typically majority rule - it's often plurality rule. Eg USA. 40% can be the winner if 2nd and 3rd place only have 30%).

Taking their table of vote totals:

Candidate Votes For Votes Against
Alice 501 499
Bob 3 0
Charlie 496 501

An arrangement of ballots that produce that in preferential voting would be:

  • 501 x ABC (501 for Alice, 501 against Charlie).
  • 496 x CBA (496 for Charlie, 496 against Charlie).
  • 3 x BCA (3 for Bob, another 3 against Alice).

Following the rules of preferential voting, A wins immediately (more than 50% of the 1st preference vote), but were we to distribute preferences anyway; B is removed, all first preference B (only 3 x BCA) votes are removed, and 3 2nd preferences flow to C. Alice wins by 2 votes.

For a democratic voting system the plurality must win, and that applies to all 3:

  • The plurality (50.1%) voted against Charlie, so he shouldn't win.
  • The plurality (50.1%) voted for Alice, so she should win.
  • The plurality (99.9%) didn't vote for bob, so he shouldn't win.
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    $\begingroup$ Is it bad that I know exactly which five parties you're alluding to here? $\endgroup$
    – Sora2455
    May 9 at 23:07
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    $\begingroup$ @Sora2455 was going to go with "Mrs Hitler", but their candidates in my state are all white straight males. $\endgroup$
    – Ash
    May 10 at 1:15
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    $\begingroup$ That's not really accurate, though, because low votes don't get subtracted from the high votes. They just don't get added to their totals when your vote is counted, as long as you've listed one of the top two parties before then. Also, the Greens are far-left communists, not mid-left, but this isn't really the place to discuss real-world politics. $\endgroup$
    – nick012000
    May 10 at 5:21
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    $\begingroup$ @nick012000: “low votes don’t get subtracted from high votes” — That doesn’t make a difference. If each voter gives candidates (say) 3, 2, and 1 points, that gives exactly the same winner/loser in the end as voters giving candidates +1,0, and –1 points. $\endgroup$ May 10 at 8:36
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    $\begingroup$ @nick012000 Your objection would be valid if you indicated your top 3 preferences, and then left the rest blank. Once you introduce the requirement to rank all candidates, it becomes equivalent to ± system, but pivoted around the average result rather than 0 $\endgroup$ May 10 at 9:17
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There are so many different and well studied voting systems, each one with its particularities. For instance, this site presents a single election evaluated with 4 different methods which gives 4 different results.

Many of the existing methods allows for voting against a candidate, either explicitly or by placing one candidate in disfavor in relation to the others. Other answers already explained how it is done in a Condorset method: you rank the candidate you disfavor lower than the other candidates. But let me talk about one of my favorites voting methods: approval voting.

A voter must choose either 👍 or 👎 for every candidate in the ballot, representing if that choice is acceptable or not. In the end, wins the candidate with the average closer to 👍.

This is a very good system that combats polarization and have many good mathematical properties, like being resistant to tactical voting and not being possible to hurt your candidates by going to vote instead of not going.

Save for psychological factors and abstentions, this method is equivalent of allowing for voting to many candidates at once. In such scheme, voting against someone would mean voting for everybody else.

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Your election system is affine, which means adding 1000 to every candidates vote total doesn't change the result. The highest value wins.

We can translate your vote from -1/0,0,0,0/+1 to 0/1,1,1,1,1/2 and get the exact same result. Except now we can see why it results in strange results when there are many candidates.

If you like party A and think you have a good chance of helping them win, you'll give them a 2.

You now give 1 vote to everyone else. Finally, you pick a party you think could beat party A and you don't want to. They get a 0.

Now, suppose you have two wings of politics -- Up and Down. The Up wing has its power concentrated in one party -- the Top party.

The Down wing of politics has 5 different parties who all mostly agree that the Up/Top sucks, but disagree on details.

When someone wants to support Up, they give it 2 votes, and then ... they give each of the Down 1 vote, except whomever they think is most dangerous to Up.

When someone wants to support Down, they give one of the Down parties 2 votes, and give the Top party 0 votes. And they give every other Down party 1 vote.

The Down parties in a sense "get votes" by being split up.

Suppose we have 100 Up supporters and 100 Down supporters. The Down supporters vote semi-randomly -- between 10 and 30 vote for each of the 5 parties.

The Up supporters don't know exactly how the Down supporters vote. So they end up spreading their "anti vote" over each of the down evenly.

At the end of the cycle we have:

Top: 100 yes votes, 100 no votes.  Total: 200 (or 0).
Down1: 10-30 yes votes, 140 to 160 neutral votes, 20 no votes, total: 190-210 (or -10 to 10).
Down2: the same

The result will be one of the Down parties winning just due to variance.

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In a two-party system you would see even dirtier election campaigning than you see in the United States. Candidates would not just want people to vote for them as the lesser evil, they also want them to vote against their biggest rival as the greater evil. That would make attack ads even more important for winning elections than they already are.

However, in a multi-party system, it might be a good idea for the two strongest candidates to form a pact to not run any attack ads against each other and instead attack the candidates of the minor parties. Otherwise you risk that each of them receives as many positive as negative votes and a minor party candidate wins.

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Of all the electoral systems that have been in wide use and documented, none are exactly like what you proposed. By the way, according to that Wikipedia page, "the study of formally defined electoral methods is called social choice theory or voting theory, and this study can take place within the field of political science, economics, or mathematics, and specifically within the subfields of game theory and mechanism design."

people vote for their favourite candidate and against their least favourite. The against votes are subtracted from the for votes.

First of all, "least favourite" does not explicitly mean "against."

If that's all there is to your proposed electoral system, then, to clarify, you're saying voters are required to make two, and only two, marks or voice-votes for a race: one mark denoting their favorite and one mark denoting their least favorite. It means either the amount of candidates has been restricted to two or that the voter is not allowed to vote for their "middle-weight" candidates about whom they feel more ambivalent. It's different from all presently notable voting systems.

Instant-runoff voting, known in the United States as ranked-choice voting and asserted by two of the answers previously offered to you that have at present the two highest numbers of approval votes from registrants to this website, is not what you proposed. In that system, the amount of marks may be optional, full (every candidate requires a mark), or partial (N marks, where N is less than the amount of candidates on the ballot for that race). Voters mark numbers denoting their rank of preference for the candidates. For all amounts of marks except full preferential, marks represent only approval. Marks never explicitly represent opposition or disapproval of candidates that the voter ranks lower. Further, its counting method is entirely different.

In approval voting, described by the previously offered answer that has at present the third-highest number of approval votes from registrants, marks represent approval and are decided for each candidate individually, not in ranking or comparison to other candidates. Some ballots for this system may ask voters to mark "No," which represents, "I do not explicitly approve." A blank or "No" does not explicitly represent opposition or disapproval because the counting and calculation method used by this system recognizes only marks of approval.

So beyond variables that precede these such as who is allowed to vote and how difficult it is to be allowed, there are variables in the format and layout of the ballot; variables in the amount, representation, and meaning of marks or blanks; and variables in the method and verifiability of... recognition, counting, and calculation.

As far as mathematical criteria, you can find most of them on Wikipedia's comparison of electoral systems. tl;dr: Jump down to the first table, or click the "Comparisons" heading. In my opinion, this is the best place to start of all the information I've read.

Two of the criteria for electoral systems that are often overlooked but I think are very important with the rise of voting machines are polynomial time and summability. In the context of electoral systems, polynomial time and summability basically tell you whether counting and verification by recounting can be done through a distributed method ($O(n)$) by each tier of polling districts verifying their district... or that counting and verification can be done only at one top-most central location ($O(n^m)$) to which is shipped every marked ballot or a copy of data from every ballot cast in the election. The location could be a warehouse filled with the marked ballots or a mainframe computer storing a database file.

Instant-runoff (ranked-choice) can be counted only at one top-most central location. If IRV was counted by hand and not by machines, a central location could allow better oversight than a distributed count, but ballots are not usually counted by hand anymore. They're counted by profit-influenced, proprietary, closed-source software on black-box hardware. Campaign officials, scrutineers, polling place volunteers, and most election officials are not known for being skilled in information security, cryptography, computer engineering, or software engineering. There are a few skilled ones who regularly consult to a national government, the United States, at the Brennan Center for Justice.

Another system similar to your proposal is score voting. Score voting that's been reduced to a three-point scale (approve, neutral, oppose) is used by Wikimedia's Board of Trustees and by the United Nations to select the UN Secretary-General. However, its marks are decided for each individual candidate, not explicitly in comparison to other candidates as your proposal is.

One more notable system, Schulze method, is used by ICANN, many free and open-source software projects, the Pirate Party in many countries, and the self-governing bodies of several languages of Wikipedia. It's one of the few systems that satisfies most criteria, but it's one of the most complex in polynomial time.

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