negative voting

Last week, a group of prominent figures, including Shih Ming-teh 施明德, Sean Chen 陳沖, and Su Chi 蘇起, proposed that Taiwan should employ a new electoral system, which they called “negative voting.” As I understand the proposal, this is intended for single seat elections. Each voter would still cast one vote. Currently, the vote must be a positive one, so that each vote increases the candidate’s total by one. Under this proposal, the voter would have the option to either cast a positive or a negative vote. A positive vote would increase a candidate’s total by one, while each negative vote would decrease the candidate’s total by one.

If I understand correctly, some variant of this system is sometimes used in elections for board of directors of corporations. I do not know of any sort of negative voting used in elections for public offices. (The closest thing I know of is Approval Voting, a system invented and promoted by a couple of professors at New York University. In Approval Voting, the voter can vote for as many candidates as he or she approves of. If you vote for all but one, that is mathematically equivalent to a negative vote for that candidate. However, since a voter can cast different numbers of votes, approval voting differs from the proposed negative voting in important ways. I don’t think Approval Voting has been adopted for any elections to public offices.)

Let’s look at how this system might affect who wins or loses. If there are two candidates, negative voting really doesn’t make any difference. If you prefer A to B, you either vote positively for A or negatively for B. This system is designed to affect races with at least three candidates, so let’s delve into that. Assume there are three candidates. A is a leftist, B is a centrist, and C is a rightist. If the polls say that A, B, and C have 40, 30, and 30% support respectively, we can normally expect A to win. A’s supporters are happy with this and will go ahead and cast positive votes for A. B’s supporters know that B is losing, but they don’t have a clear second favorite candidate. Some of them prefer A to C, and some prefer C to A. They could hedge their bets and vote negatively against their least favorite candidate. Mathematically, this would be equivalent to voting for both B and their second favorite candidate. C’s supporters have a much easier choice. They all prefer B to A, so they can simply vote against A. If all of B and C’s supporters vote negatively, we thus get A: -5%, B: 0%, C: -15%. So B wins with zero votes?? Hmm. I wonder if the proponents of negative voting considered what would happen if the “winner” got zero or even negative votes. That seems like an outcome the PRC would love to see! (Note: B also wins A:10, B: 30, C: 0 if A’s and B’s supporters cast positive votes and only C’s supporters cast negative votes.)

Vote totals aside, the important point is that the new system changes the outcome. Instead of the leftist (who led in first preferences), the moderate is now the winner. Some people see this as a desirable outcome. In technical jargon, B is the Condorcet winner. That is, B wins the head to head matchups against all the other candidates. (In a one on one matchup, B beats A, 60-40, and B beats C, 70-30.) Negative voting empowers moderates! Hooray!

Not so fast, but hold that thought while we first explore a different idea.

Negative voting will be most useful to factionalized parties who cannot agree on a single candidate. Image that party A has a majority in society (A: 55; B: 45), but it has two big factions that will not yield to each other. Eventually both candidates, A1 and A2, both decide to run. Assume that the first preferences now break down as follows: A1: 30, A2: 25; B: 45. In a plurality race, B is going to coast to an easy victory. However, if 80% of party A’s voters vote negatively, they can avoid losing to B, even though they were unable to resolve their intra-party squabble. The result would be A1: 6, A2: 5, B: 1.

I think this is the real purpose of the proposal. People inside the KMT fear that the Wang and Ma factions are terribly split, and they will not be able to cooperate (perhaps even if Chu runs). Or perhaps Ma simply wants to run his own candidate. Negative voting avoids the problem of resolving intra-party tensions by simply allowing KMT sympathizers to vote against the DPP. Of course, this assumes that the KMT is still the dominant party. I understand that many people within the KMT believe that the voters will come back to them when real power (ie: national power) is at stake, though I suspect they are fooling themselves. I think their fundamental problem is that Tsai Ing-wen might have over 50% of the votes, not that the pro-Ma and anti-Ma factions can’t cooperate. At any rate, I think there is tremendous value in forcing a party that wants to hold governing power to first be able to resolve basic internal conflicts. If a severely factionalized party wins power, will it be able to effectively govern?

Let’s go back to that idea about negative voting encouraging moderates. Imagine a two candidate race, with A narrowly leading B by 52-48. What could B do to change the outcome? What if an extremist candidate BB on B’s side of the spectrum jumped in? In a normal plurality race, this couldn’t help B at all, since any votes BB won would almost certainly be taken from B. However, with negative voting, it might be different. Imagine BB is a terrible person, spewing all sorts of offensive and inflammatory rhetoric. BB would be all over the news, and voters would be outraged. In fact, some might come to the conclusion that it is important to resoundingly reject BB’s horrible ideas. However, those negative votes against BB would probably come predominantly from A’s side of the spectrum, since BB’s ideas would naturally be extremely offensive to them and only moderately offensive to voters on B’s side of the spectrum. If BB won positive support from 1% (originally B voters), while 7% of A voters and 1% of B voters decided to make a statement by voting against BB, the result would now be A: 45, B: 46, BB: -7%. BB would in fact be resoundingly rejected. However, this would also throw the election to B.

I think most of us can agree that democracy is not well-served when vile extremists can affect the outcome of a race by hurting the chances of the mainstream candidate on the other side of the spectrum. This is why positive voting, in which voters have to support something, is the norm. With positive voting, candidates are not rewarded for being offensive. With negative voting, the more offensive a candidate is and the more voters that are shocked into rejecting him or her, the more power and influence that candidate has.

To put it bluntly, this proposal for negative voting is a terrible idea.

A short comment on the idea that negative voting would save money: Candidates/parties currently get NT30 for each vote, so negative voting would supposedly reduce the public subsidy.

I’m starting to believe that the surest sign that some proposed electoral reform is a bad idea is that its proponents stress how much public money it will save. It seems almost like they are trying to distract us from their weak arguments about why it will produce better politics with shiny, shiny money!

There is a good reason for the public to subsidize parties. We have a general interest in parties that have the capacity to do things like formulate policy platforms. Bureaucracy and think tanks cost money. Back in the mid-1990s, when Shih Ming-teh was DPP party chair, the DPP could barely afford to pay rent. His predecessor Huang Hsin-chieh 黃信介 routinely wrote a personal check to cover the DPP’s monthly operating costs. That party struggled to avoid bankruptcy; it certainly did not have the capacity to do long term planning or prepare a broad set of policy proposals that it might pursue if it were to become the governing party. Shih seems currently to be arguing that the public subsidy is a waste. I disagree. I don’t want to return to the days in which there was only one party with the capacity to govern.

45 Responses to “negative voting”

  1. ジェームス (@jmstwn) Says:

    “I think there is tremendous value in forcing a party that wants to hold governing power to first be able to resolve basic internal conflicts. If a severely factionalized party wins power, will it be able to effectively govern?”
    I hadn’t thought of it like that before. That’s very compelling. By that logic, are you against two-stage elections (first everybody, then a runoff between the 2 strongest) like the kinds used for the Brazilian and French presidents and the Mayor of Chicago?

    • frozengarlic Says:

      I’m not crazy about runoff elections precisely since they discourage pre-election aggregation. In fact, they actually encourage fragmentation since minor parties or factions will run a candidate precisely to demonstrate their strength so that they can bargain with/blackmail the serious candidate. I prefer the Argentine rule. If the candidate with the most votes in the first round has at least 45%, that candidate wins. If the leading candidate has less than 45% but the gap between first and second candidate is larger than the distance between the first candidate and 50%, the leader wins. Otherwise the top two candidates go to a runoff. For example, if A has 43%, B has to get at least 36% to force a runoff. This method forces parties to make coalitions before the election or risk losing. At the same time, it is very hard to win in the first round if you can’t get at least 40% or so. (I like this system for two reasons. First, it works. Second, my former professor, Matt Shugart, invented it. Score one for political science!)

  2. David on Formosa Says:

    I can see that the negative voting system you suggest is problematic. I still don’t understand why there is not more interest in preferential or ranked voting. It works very well in Australia but many other democracies seem to spurn it. I think non-transferable voting systems which force voters to vote tactically rather than express their true preference are also anti-democratic.

    • frozengarlic Says:

      There is a great fear that preferential votes are too complicated for ordinary voters to understand. If you look at the survey data, voters can’t really even understand the relatively simple MMM system that Taiwan has now. I think this is overblown. Voters will figure out how to vote appropriately (with a lot of education from the CEC and, more importantly, parties and candidates). They certainly seem to have figured out how to vote in the current system. At the same time, I do acknowledge the idea that electoral systems for public elections should be as simple as possible so that even people with minimal education can understand them. It’s one thing to ask shareholders to use a Borda Count to elect a board of directors; it’s quite another thing to try to explain to Grandma who can barely read and/or isn’t mentally all there that she can give nine points to one person, eight to another, seven to another, and so on.

      Personally, I’d love to see an Irish-style single transferable vote system (with preference votes and multiple seat districts). I’m not as crazy about the Australian alternative vote (which has been reinvented in San Francisco as the “instant runoff”) which has preference votes but only one seat. I don’t have any active dislike for AV; I’m just not very enthusiastic about any single seat system. However, I don’t think either is going to happen in Taiwan any time soon. Neither, for that matter, is negative voting.

      • David Reid Says:

        There is a great fear that preferential votes are too complicated for ordinary voters to understand.

        I must admit even in Australia where the system is widely used there are a lot of misunderstandings about how it works. I think a lot of this is due to obfuscation and misunderstanding promoted by the two major political parties and mainstream media who want to maintain the status quo and lock smaller parties out of power. That said, particularly in the Senate, more and more Australians are voting for minor parties in an expression of dissatisfaction with the current two party system.

  3. Clay Shentrup Says:

    This system is actually called Evaluative Voting, and it is a form of Score Voting. It is an incredibly good system according to Bayesian Regret calculations from a Princeton math PhD named Warren Smith.

    Score Voting is just rating the candidates on a scale, such as 0-5 or 1-10.

    Approval Voting is technically just Score Voting on a 0-1 scale.

    Evaluative voting is Score Voting on a -1 to +1 scale. It is mathematically the same as if you could rate the candidates on a scale of 0-2. (Although there are psychological differences between the lowest score being 0 or a negative number.)

    Clay Shentrup
    Co-founder, The Center for Election Science

    • frozengarlic Says:

      Thanks for the comment. If I understand correctly, the proposed “negative voting” is not the same as your score voting. In approval voting (which is a variant of score voting), the voter can express an opinion on each candidate. In this proposed negative voting, the voter can only express an opinion on one candidate. This difference drives most of the discussion in my post.

  4. ジェームス (@jmstwn) Says:

    The list of DPP registrants for the legislative races is out:

  5. Clay Shentrup Says:

    Only one candidate? That is certainly bad. I misunderstood and thought you could evaluate _every_ candidate.

  6. Clay Shentrup Says:

    Here are two proportional systems that are better and simpler than STV.

  7. Clay Shentrup Says:

    As for complexity, this system is certainly simpler than STV, which you’re advocating. Consider this:

  8. Warren D Smith Says:

    If I understand it right,this voting system is the same as the plain plurality voting system when 2 candidates, and the same as “approval voting” system” when 3 candidates, but when 4 or more candidates, it differs from either (and in my opinion is not as good as approval voting). Definitions:

    Plurality voting: Your vote is “name one candidate then shut up.”
    Candidate with the most votes wins.

    Approval voting: Your vote is: for EACH and every candidate, you either “approve” or “disapprove” them. (If election is A vs B vs C vs D: you could approve A & B, disapprove C & D.) Most-approved wins.

    Score voting aka Range voting: Your vote is: you give a numerical SCORE within a fixed pre-agreed range (for example the set {0,1,2,3,4,5,6,7,8,9}) to each candidate,
    (If election is A vs B vs C vs D: you could score A=9, B=9, C=7, D=0.) Greatest average score wins.

    Negative voting (if this is what you meant): Name one candidate and give him either +1 or -1. Candidate with greatest sum wins.
    The negative voting system was proposed by a political scientist named Boehm in a paper which I think was never officially published:
    George A.W. Boehm: One Fervent Vote against Wintergreen, manuscript 1976.
    Boehm’s system then was pretty much abandoned by voting system reformers because the consensus became that approval voting or score voting were better.
    However, as I said, it happens to be equivalent to approval when 3 candidates, and equivalent to plurality when 2.

    Score voting with 3 score levels was already used in Renaissance Venice for centuries, apparently highly successfully, but unfortunately was abandoned by later world governments, most of
    which were a lot less successful for a lot less time than Venice.

  9. Warren D Smith Says:

    It says in this obituary that George A.W.Boehm was an expert bridge player, math/science
    writer, and editor of Newsweek Magazine and then Scientific American.

    Apparently Boehm privately circulated his “wintergreen” manuscript about “negative voting” among political scientists in 1976 which inspired them to invent approval voting. Actually, approval
    voting had already been invented (and score voting too) before the political scientists “invented” it, but they did not realize that for many years.

  10. Tien Shang Chang Says:

    I am the Secretary of the Negative Vote Association mentioned in your blog. Our proposal is politically neutral and not intended to target any particular political party. In the formative stage of our organization, we tried to get other notable persons to serve as our Chairman, all declined except Shih, probably for the very reason that the Chairman would be a target of attack from both political parties. The result is indeed that. Two DPP legislators’ criticism was simply more vicious (in order to draw attention to themselves). All KMT legislators asked by reporters also objected to our proposal, as expected.

    We believe Negative Vote should be adopted for three basic reasons:
    1. The fundamental right to say No in any democracy

    If there is only one candidate, and we can only say yes, you’d think we are living in North Korea. In the last election in September of 2014 in Taiwan, 38% of the lowest election office (村里長), or 2970 persons ran unopposed. I am sure most of these persons are so loved by their neighbors that they are unopposed (one of our founders is such a person). Yet, it is also public knowledge that some of these are the local ganster boss who can intimidate others from running against him. Negative Vote will solve this problem. None of the mathematical calculations you mentioned in other systems can solve this problem.

    I’ll write more later to get into other reasons to adopt Negative Vote. Welcome any feedback on this first point.


    Sam Chang

    • frozengarlic Says:

      Thanks for the explanations, Sam. Let me respond to your first argument.

      There is no such thing as a fundamental democratic right to say no. Such a right could undermine the very system. Consider present-day Greece. There is no political force with anything close to a majority. Greeks are deeply fragmented, and clear majorities oppose every party. If they had the right to reject, they would almost certainly reject every option, again and again. No government could form, and the democratic system would eventually collapse.

      The fundamental democratic right is to elect, not to reject. This is a positive right, not a negative right. If you are dissatisfied, you are free to organize similarly dissatisfied people to put someone better in office. This is very difficult, since it usually forces you to make compromises in order to cooperate with people you only partially agree with. However, those compromises are an essential part of the democratic process.

      Organized crime should be dealt with directly, through direct intervention of the criminal justice system. Negative voting is not going to solve that problem. As to all the uncontested elections for 村里長, frankly I think that is a pretty good indication that the office is unnecessary and should be abolished.

      PS: Taiwan is nothing like North Korea.

  11. Warren D Smith Says:

    Rather than a “fundamental right to say no,” better would be “a right to say what you, as a voter, feel about all the available options.” Because the purpose of democracy is to assess voter
    opinions and make the right choice, the better voters can express their opinions, and the better those opinions are combined to produce a choice (election winner) the better the world will be.

    Unfortunately with “plurality voting” rules, voters CANNOT
    say their opinion of any candidate besides just one. That is one reason plurality is an extremely poor voting system. Negative voting is a little better, but still suffers the exact same problem: voters CANNOT say their opinion of any candidate besides just one. With score voting voters can say their opinion of every candidate, and say it using a graduated scale (0123456789).
    That’s a lot more and better information.

    Is score voting too complicated? It has been successfully used by kindergarteners. It was tried in a multi-voting-system experiment in France with 1000s of real voters, with the result that the voters preferred it over the present French system. It experimentally produces fewer “spoiled ballots” (errors) than plurality voting.

    You can learn a lot more at the score voting web site
    (site has search box) or the French-language score voting site founded by several political science professors
    In particular the kindergarten experiment is here:

    Click to access ShermanPetElection.pdf

    The French multi-study is discussed here:
    Spoiled-ballot rates here:
    and “what systems voters want” here:

    You can email me at warren.wds AT with questions,
    or join the CES (center for election science) forum, where everybody will answer your questions (or claim to):!forum/electionscience

    Now about the “Negative Vote Association” (NVA) in Taiwan, I
    will now comment about the following news article:
    “New NGO launches campaign to allow negative votes in elections”
    Taiwan Central News Agency, 2015-3-1,
    authors Tai Ya-chen, Hsieh Chia-chen, Elizabeth Hsu.
    I am very pleased that prominent figures in a prominent political party are urging voting-system reform. Unfortunately it does not look to me like they’ve made a serious study of different voting systems (in particular nobody contacted me) and therefore just invented one based largely on intuition seasoned with too little knowledge. That’s dangerous. Voting systems have been studied over 100 years and there are books and web sites on the topic.
    Intuition is often wrong in this area.
    QUOTE: The idea of allowing “no” votes in elections, which he described as “very progressive and original,” was first proposed by several “well-known intellectuals with successful careers,” Shih said in answering questions from reporters.
    No, idea is *not* original, it dates to Boehm 1976, and in the view of practically all actual experts in this area, the negative vote system is now obsolete having long ago been supplanted by Approval and Score voting. (The fact the NVA does not know the 40-year history of its “own” idea seems not a good sign.)
    QUOTE: A voting system should be as simple as possible, Ker said… inclusion of negative votes will make the electoral system more complicated, Lai argued, saying that it might take voters time to learn the new mechanism.
    Simplicity can be assessed by experiments, not intuitional guesses.
    One metric is how often voters make ballot-invalidating errors.
    By that metric both approval and score are better than plurality, despite naive intuition they are more complicated. Another metric is speed: how rapidly do people vote? Again, surprisingly, ratings are produced faster than head-to-head “who’s better” choices (despite providing more info!) according to the “hot or not” experiments:
    (The “hot or not” website was founded by Asian-American entrepreneurs Hong & Young, became a cult favorite, was fun, then they sold it for $20 million and now it is no fun anymore.)
    Another metric is how voters themselves regard the method when asked how simple it is. All studies and metrics agree that score and approval voting both are simpler than “instant runoff” but the latter has been used in Australia and Ireland for over 80 years. So it is not unacceptably complicated. “Negative voting” has not, far as I know, been studied in these ways; the fact over-voting is illegal with it, and the use of negative numbers, both are dangerous for inducing errors and ballot spoilage. (With approval and score, “over voting” is impossible and negative numbers never needed.) Voters prefer score over approval voting, and prefer 10-level score sets over other numbers of levels:

  12. Tien Shang Chang Says:

    The second reason Negative Vote should be adopted is that voter participation will increase. Voluntary increase in voter participation is good for democracy. Under the current system, many voters who dislike any of the candidates can only choose to stay home and not go to the polls. Their voices are not heard at all. I think this is one of the main reasons voter participation has declined in many democracies.

    Under the current system, the winner often arrogantly proclaims “I have majority popular mandate” but the truth is usually he does not. Because many people who dislike him did not vote. Some voted for him as the “lesser of two evils”.
    If Negative Vote is adopted, winner is the person that gets the higher net positive votes. Whoever wins is likely to see some people voted against him and hopefully become more humble in governing.

    Better minds than mine have written about this before, see the following article:

    Daniel Ferguson & Theodore Lowi (2001): Reforming American Electoral Politics: Let’s Take“No” for an Answer, 34 PS: Pol. Sci. & Pol. 277, 277

    I apologize for responding in piecemeal fashion. The fact is I have to focus most of my attention to our organization’s effort in Taiwan. I’ll try to squeeze some time to respond further. Thank you for your patience.

    • frozengarlic Says:

      There are two separate points here, that negative voting will raise turnout and that it will prevent politicians from claiming to have popular mandates.

      I agree that negative voting would raise turnout a bit. However, I think the effect would be small. Currently, the highest turnout rates in Taiwan are in presidential elections, where turnout has ranged from 74% to 82%. Many Taiwanese citizens live outside Taiwan — perhaps as many as three or four million — and most of these will not return to vote. That means that almost all eligible voters in Taiwan have actually voted in a single seat plurality election with only two or three choices. I suspect that the lower turnouts in other elections are more due to lack of interest than to disgust with choices. When lower-level elections are combined with higher-level elections, the turnout rate for the lower-level elections goes up dramatically. This indicates to me that the problem is one of mobilization, not unacceptable options.

      On mandates, you have a point. Presidents often claim a popular mandate, and they would have a harder time making this claim if negative votes pushed their aggregate totals down significantly. On the other hand, sophisticated legislators probably already make this calculation when they decide whether or not to support the president’s proposals. For politicians in offices lower than the presidency (and maybe the Taipei City mayor), I doubt a mandate matters very much. Their power stems from the formal powers of office more than any popular mandate.

  13. Tien Shang Chang Says:

    The third reason Negative Vote should be adopted is that it will reduce extremism.

    Negative Votes are more likely cast by the middle electorate against extremist candidates. Extreme rhetoric will therefore reduce over time. A society will become more harmonious internally and less likely to go to war against its neighbors.
    Negative Vote will therefore enhance harmony and world peace.

    For those who are interested in joining an academic discussion about Negative Vote, I recommend Jess Brewer’s website. Jess apparently had come up with the idea independently in 2007.

    • frozengarlic Says:

      I agree that most negative votes will be cast against extremists. Paradoxically, I fear that this may encourage more extremist candidates to run. Instead of voting for a moderate KMT candidate, a blue voter might be tempted to vote against a radical TSU candidate. A negative vote against a radical TSU candidate is neutral concerning the moderate DPP and KMT candidates. Thus, from the DPP’s point of view, if the radical TSU candidate can be so offensive to cause the blue voter to vote against him, the DPP candidate benefits. The TSU also benefits, since they prefer the DPP to the KMT. Thus there is an incentive to run as an extreme radical. (This situation is exactly parallel on the other side of spectrum.)

      In the score voting that the other commenters are advocating, this is less of a problem. In that system, you cast a vote (for or against, 0 to 10) for each candidate. Thus, our hypothetical blue voter could give the offensive TSU candidate 0, the moderate DPP candidate 4, the moderate KMT candidate 8, and an extremist New Party candidate 5 points. Rejecting the offensive TSU candidate does not help the DPP candidate.

    • frozengarlic Says:

      By the way, many of the commenters on Jess Brewer’s discussion are confused; strictly speaking they are not talking about negative voting. Many of them are talking about striking off names on a party list in an Open List Proportional Representation system.

      Taiwan currently uses party lists to elect 34 seats in the legislature. If a party gets 50% of the party list votes, it will get 17 seats. These go to the first 17 people on that party’s list. Taiwan has a Closed List system, so the parties give a ranked list to Central Election Commission. That is, the party decides who is #1, who is #2, and so on. In other countries with open lists, the parties send an unranked list of names to the election commission. Voters vote for a party, but then they also vote for a name on the list. The name with the most votes is ranked #1, the next name is #2, and so on. Commenters on the discussion group are talking about negative voting for the list. However, this “negative” vote is still a positive vote for the party. It still helps the party win more seats. It merely affects the order in which the candidates are ranked on the list. This is something different from negative voting in a single seat plurality election.

  14. Tien Shang Chang Says:

    The above 3 reasons apply to all democracies in the world. For Taiwan we can add two more reasons why Negative Vote should be adopted.
    A. If Negative Vote is adopted in Taiwan, public funds given to the candidates individually(NT$30 per vote) and their political parties(annually) will be reduced. Under the current system where we can only vote “YES”, we find our tax money going to the candidates even if we do not support any of them, because we cannot vote “NO”. If Negative Vote is adopted, such tax dollars can be saved for other more worthwhile public expenditures that really serve ALL the citizens.
    B. It is common knowledge that illegal vote-buying is still rampant during elections in Taiwan. “Negative Vote” will be very difficult to purchase. Overtime it will dilute the effectiveness of vote buying and render it obsolete.

  15. Tien Shang Chang Says:

    I’ll now start to address some of the points made in your article:

    Your wrote: “Let’s look at how this system might affect who wins or loses. If there are two candidates, negative voting really doesn’t make any difference. If you prefer A to B, you either vote positively for A or negatively for B. ”

    I disagree. While you are concerned with just the outcome of an election of who wins, we are concerned with more than that. With Negative Vote, the probability exists (though very low) that no candidate receives any net positive votes. In which case, election should be re-held and those who have been rejected should be barred from participating. The natural question to be raised in that scenario is “Would not that be very costly to the society?” To which, our response is “Isn’t electing the wrong person even more costly to the society?”

    In addition, in a two candidate scenario, under the current system the winner often arrogantly proclaims “I have (overwhelming) popular support”. The truth is more likely he does not. Many people did not vote because they dislike both. Some voted for him as “lesser of two evils”. If Negative Vote is adopted, more people would participate in voting, the result would more accurately reflect more people’s views. The outcome of who wins could also be just the opposite of the outcome when only positive votes are allowed.

    Clay S. TAKE NOTICE HERE. The math is different from Approval Voting which you advocate.

    Current system (67 voters choose to vote)
    A gets 34
    B gets 33

    (A wins and claims 50.7% majority support)

    With Negative Vote as an option (33 more persons choose to vote)

    A gets +34 and -22, net positive 11
    B gets +33 and -11, net positive 22

    (B wins and humbly notes that he does NOT have majority support)

    So your statement of “If there are two candidates, negative vote doesn’t make any difference” is not correct.

    • frozengarlic Says:

      If there are really large numbers of voters who would cast negative votes but are not willing to cast positive votes, you are correct that negative votes could affect the outcome of a two-candidate race. I am skeptical about this assumption.

    • waughuspolitics Says:

      Comparing a Negative Vote “two-candidate” race to an Approval Voting two-candidate race is not an apples-to-apples comparison, because in the former case there are actually three possible outcomes: Person A wins, Person B wins, or the election is thrown. As a two-candidate race in Approval would normally be understood, the election could not be thrown; one of the human candidates would win unless they tie. If you want an apples-to-apples comparison between the systems as applied with an example of two human candidates, and if it still must be possible for the Negative Vote election to throw the election, then the fair comparison would be to an Approval Voting election with three candidates, two of whom are the human aspirants, and the third of which is a command to throw the election. In such a comparison, could we cast the Negative Vote election as equivalent in terms of the powers granted to the voters, to a version of the Approval Voting election with additional constraints of some sort imposed on the ballots that are not part of the definition Approval Voting? I’m not sure. Even though I don’t know the answer, it’s not an ambiguous question. It’s mathematically provably either true or false.

  16. frozengarlic Says:

    Tien Shang, thanks for explaining your ideas in such depth. I mostly disagree with you, but I am glad we can have such an interesting discussion.

  17. Tien Shang Chang Says:

    For more academic discussion of Negative Vote, I recommend you check Jess Brewer’s website:
    Jess apparently thought of this idea independently in 2007. I did also in 2011 then started to research into this more seriously in 2013. I discovered along the process, not only Boehm, but Felsenthal, Brams, and the others mentioned already, and a Mr. Ferng in Taiwan who wrote of this idea in 2004 also independently (like Boehm’s article, never published). Ferng is one of the co-founders of our organization. Warren Smith suggested that the Negative Vote idea was studied and rejected by consensus. I could not find any evidence of the idea ever being studied or even discussed at any length, except on Jess Brewer’s website. Perhaps someone on this forum can enlighten me how it was studied and why it was rejected by whose consensus.

    • frozengarlic Says:

      Warren Smith’s statement that negative voting was found inferior to approval voting and score voting seems reasonable to me. I don’t know this literature, since mathematicians and political scientists tend to ask very different questions. Mathematicians tend to be concerned with whether a voter’s choice can help him to elect a more preferred candidate. You can see from Smith’s links that he is worried about things like “voter regret.” From this perspective, approval voting and score voting are clearly superior to negative voting. (Almost everything is superior to ordinary plurality voting.)

      Political scientists tend to ask questions about how the electoral system will transform the political system. For example, we want to know if a particular system will represent small parties proportionally, whether it will strengthen or weaken internal party discipline, or whether it will encourage corruption.

      Politicians, of course, usually ask whether a system will help them win more power or not. One reason they don’t like more complicated voting systems, such as score voting, is that their most reliable and loyal voters tend to be either ideologues (who can generally figure out any system) or voters embedded in mobilization networks. The latter are often older, less educated, and less sophisticated, so politicians want to make the choice as simple as possible for these people. It really doesn’t matter how many computer simulations or kindergarten classes you show them, most politicians just won’t be willing to risk a more demanding choice.

      From this perspective, even though your negative voting is mathematically inferior to score voting, it probably has a better chance of being adopted. Politicians are attracted to simplicity. Of course, the current system is even simpler.

    • afds Says:

      The system you’re proposing is NOT the same as Felsenthal’s (Evaluative Voting / Combined Approval Voting). You only allow voters to cast one vote, for or against one candidate, while this other system allows you to vote for or against EVERY candidate. It’s a big difference, and your system is not nearly as good.

  18. Tien Shang Chang Says:

    The concept of Negative Vote is sometimes referred to as: CAV(Combined approval voting), Bipolar Voting, or Formal Recognition of the Negative Preferences

    Following are various English language sources that specifically deal with the Negative Vote concept. For English articles, I recommend the Ferguson/Lowi article.

    1. Boehm, G.A.W. (1976): One fervent vote against Wintergreen. Mimeograph. (I could not find a copy)
    2. Brams, S.J. (1977): When is it advantageous to cast a negative vote? In: Mathematical Economics and Game Theory: Essays in Honor of Oscar Morgenstern (R. Henn, O. Moeschlin, eds.). Springer, Berlin, pp. 564–572.
    3. Felsenthal, D.S. (1989): On combining approval with disapproval voting. Behavioral Science 34, 56–70.
    4. Daniel Ferguson & Theodore Lowi (2001): Reforming American Electoral Politics: Let’s Take“No” for an Answer, 34 PS: Pol. Sci. & Pol. 277, 277
    5. Jess Brewer
    7. Michael Kang(2010): Voting as veto, Michigan Law Review, Vol. 108, No. 7

  19. Tien Shang Chang Says:

    There has been repetitive assertions in this forum that Negative Vote is inferior to approval voting mathematically. I have not seen any proof of that. Perhaps someone can direct me to such a proof. Artificially changing the definition of negative 1 to 0 or any other value does not count as proof. If one can change definitions, one can prove anything one wishes.

  20. Tien Shang Chang Says:

    I think the sad truth is that Negative Vote was never seriously studied but dismissed out of hand callously by experts. Did anyone really take into account of increase in voter participation in their math models? In a narrow race of two persons, even a small increase in voter participation can reverse the outcome: for illustration purpose only, below is a hypothetical exaggeration to make the point

    Current system

    A gets 7,000,000
    B gets 7.000, 001

    B wins and proudly claims he has absolute majority mandate.

    With Negative Vote

    A gets +7,000, 000 but also minus 100 net 6, 999,900
    B gets +7,000,001 but also minus 200 net 6, 999,801

    A wins when there is higher voter participation of just 300 persons out of 14 million (0.002%), and admits humbly that he does not have majority mandate.

    Voluntary increase in voter participation is good for democracy, that is logic, cannot be refuted by any study.

  21. Tien Shang Chang Says:

    Negative Vote will lead to more positive results

    In your commentary as well as in Chinese press, the worry that Negative Vote will lead to more negative campaign has been expressed. We believe just the opposite would happen.

    Under the current system, candidates already resort to all kinds of negative campaign. One can do so and get away with it precisely because there no one can vote against him, no downside. By throwing dirt on the opponent, he will not lose his own supporters and he might reduce support for the opponent, and middle-of-the-road voters cannot punish him. That’s why almost all candidates resort to negative campaign tactics in some fashion.

    Under the current system, a candidate does not need to seek majority approval. Often one only needs to focus on support of passionate minority to win an election. Such minority interests are often the opposite of some other minority group’s interest. Both sides then cast negative campaign against the other and we are burdened with constant bickering. Middle electorate can do nothing and therefore do not go the polls. With Negative Vote, they will come out and vote against the most extreme elements. Extreme rhetoric will therefore be reduced. Society will become more harmonious internally and less likely to go to war against its neighbors.

    What we are proposing is therefore not just an election reform issue but something that will enhance world peace.

    Let me use a practical example how this might affect Israel. I visited Israel 4 times. During one of those trips, a local friend Ran told me that there are some people in Israel who are not subject to military draft. I was surprised so asked him to tell me more. Ran said that during the Independence War, a group of Jewish fundamentalist religious leaders went to see Ben Gurion and asked graduates of their religious schools be exempt from military draft. There were only a few hundreds then and Gurion agreed. Now of course there are far more than that. My friend Ran considers himself a middle-of-the-road voter but he feels very frustrated about this group. He said although they are a minority, they can always win in elections. They are the ones who make trouble on the streets (I presume he means demonstrations). They are the ones who refuse to negotiate with Palestinians. They are the ones who go over and occupy lands. Yet when war starts, my children have to fight and their children do not.

    Consider this: if Negative Vote is available in Israel, would middle-of-road voters like Ran vote against this group’s candidates?

    Under the current system, this group cannot see how many voters dislike them. They can only see how many support them. They will probably not change their mind on what they believe but their representative power in government should reflect reality rather than distortion which is what we have today. Not only in Israel, but in all democracies. Isn’t it true that extremist factions have a disproportionate influence in all democracies?

    Negative Vote can solve this problem.

    • frozengarlic Says:

      A couple of points.

      First, with the Israeli example, you are mixing together single seat elections and multi seat elections. (Israel does not directly elect the Prime Minister. They only elect the 120 members of Parliament in a single, nationwide district by closed party lists.) These are very different types of elections, and it is usually best to consider them separately.

      Second, think of this from the perspective of the small group. They generally don’t think of themselves as “extremists.” They usually think they are fighting a legitimate fight against an uncaring, corrupt, and unenlightened majority. They work very hard to organize a small number of people to support their cause, which they passionately believe in. After all this hard work, a small fraction of the majority votes to negate all their efforts. How will they feel? Will they conclude that democracy is a reasonable system in which they can succeed? Or will they conclude that democracy is hopeless? If it is the latter, they may decide to work outside the system, turning to even more extremist methods.

      By the way, I was surprised that Ferguson and Lowi seem to assume that most negative votes will be cast against the two major candidates and negative voting would help 3rd and 4th parties. You (and I) seem to expect the opposite to happen.

  22. Tien Shang Chang Says:

    I do not disagree with Ferguson and Lowi. They are very focused on America and I am focused on Taiwan. At both places, there are two major political parties, all others do not matter much. Middle-of-the-road voters who may cast negative votes are therefore likely to direct their dissatisfaction against the two major parties, and the smaller parties will probably benefit initially. In Singapore and South Africa, each is dominated by one single political party, I suspect negative votes will be directed against that party initially and benefit all other smaller parties. In countries with many political parties, the more extreme ones will draw negative votes.

  23. Tien Shang Chang Says:

    I believe I have addressed all questions and mis-understandings about Negative Vote expressed in this forum. I do not expect everyone to abandon his own beliefs immediately and jump to agree with us that what we are promoting is a peace movement, not just a political reform. If I missed something that I should address, please let me know. Critique is very much welcome.

  24. Tien Shang Chang Says:

    Here is one more article on negative vote written by George Leef in 2004 which I forgot to include in the previous list of references:

  25. Tien Shang Chang Says:

    Clay S. has restated his commentary related to Approval vs. Negative Voting on our group FB website.
    I’ll respond to him there as well. If you are interested, you can join us there. I am afraid though there would not be much new things to be added.

  26. Tien Shang Chang Says:

    During 2015, we commissioned Gallup to conduct 3 research polls to see what effect Negative Vote might have on the Presidential election, the party votes, and also the Hsin-Chu City district. The results can be found at our official website:
    and Facebook fans page:

    The December national poll showed voter participation will increase by 5.4%, if Negative Vote option is available, that would mean 1 million more voters coming out to vote. The same poll also showed 42.8% respondents would like to see laws changed to allow Negative Vote. This is higher than the 36.7% Tsai received in her landslide victory.

  27. Tien Shang Chang Says:

    RAND survey shows if Negative Vote option is available, voter participation would increase 7.2%, that’s 15.8 million more voters voting. Press release can be found here:

  28. waughuspolitics Says:

    As I also asked on Facebook of Tien Shang Chang and other Negative Vote advocates, how do you justify the characteristic of Negative Vote, which you could have left out of its design, that a voter cannot vote Against exactly two candidates in a four-candidate race? Shouldn’t a civil right be recognized for the voter to take such a position if desired?

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