Blanks (Xs)

Executive Summary

Voters can leave a candidate's numeric score intentionally blank by writing in X in that slot (or on a voting machine, pushing an "intentional blank" button instead of a numeric button). They might want to do that to express no opinion about that candidate, perhaps because they feel ignorant about him.

Only non-blank votes are incorporated into the average. For example if there were 5 voters and they gave scores to candidate Alice of 9, 15, "X", 72, and "X", then Alice's total would be (9+15+72)/3 = 96/3 = 32. The division by 3 is because there were 3 non-blank votes for Alice, i.e. 3 voters who wished to express an opinion about Alice.

Note that X truly has the desired effect of expressing "no opinion": If you vote X, then the societal-score for that candidate will be exactly the same as if you had never existed, i.e. will be purely determined by the other voters without you.

Some people have told me that they would have preferred 0 or 50, not X. But 0 and 50 do not express "no opinion" since they do affect that candidate's score. Indeed, 0 is equivalent to rating that candidate as "ultra bad" and is expressing a very strong opinion. But if you do want to express 0, 50, or any other opinion, go right ahead and do it. Nothing forces you to use "X"; only use X if you want to express no opinion.

Note on format

It has been suggested that writing an X is actually a very bad way to do it since voters may confusedly think X represents their vote for one candidate ("X marks the spot"). A better format to avoid that worry is to have something like this where the voter is to circle one entry per row:

Why we must have blanks

Permitting blanks is absolutely necessary to avoid spoiled ballots. Namely, suppose you enter an illegible score in some candidate's slot. (Which probably would happen a few percent of the time.) Would you prefer that

1. Your illegible score be interpreted as a "zero" thus maximally voting against that candidate (likely contrary to your intention – if you wrote something illegible, it was probably not a zero),
2. Or should it be dropped from that candidate's average ("blanked"), thus not biasing it in any way?

Why we prefer that voters write an "X" (something explicit, anyhow) – not just leave it blank

By forcing voters to write an "X", we force them to make it extra clear that they really meant it when they selected intentional blank. Also, as Andrew Gumbel pointed out in his excellent book Steal this vote, allowing voters to leave it blank is an invitation to fraud – some fraudster could just fill in the blank slot with whatever value they preferred, arousing little or no suspicion. (Of course, a fraudster could still try to alter ballots even with the X requirement, e.g. by rendering entries illegible, trying to erase them, or Xing them out, but if that happened a lot it would arouse suspicion.

How many voters are ignorant, or wish to express ignorance/indifference?

Australia: Australia has reweighted STV 10-winner senate elections and IRV single-winner house elections. In both, expressing a full preference order is compulsory. A national survey in 1979 showed that 72% of Australian voters favored the "optional" version of IRV, in which naming a single top-ranked candidate ("plumping") is permitted instead of a full ranking of all of them; only 26% favored forcing everybody to provide full-preference rankings. With plumping, the voters intentionally express total indifference or ignorance about all the non-top candidates. (They might also have wished to express knowledge or desires about several candidates, not just one, e.g. rank A top, B bottom, and C middling, and then express ignorance/indifference about the rest, but the Australian survey did not offer them that choice.)

In most of Australia, voting, and providing a full preference ranking for every candidate in every race is compulsory (monetary penalty if you do not). But IRV with optional plumping is used for state elections in New South Wales (introduced by the Wran Labor government in 1981) and in Queensland (1992). The plumping rate has increased over time in both these regions. The decision to express preferences also appears to be closely related to the recommendations made by parties on their 'how-to-vote' cards. In a survey conducted at two by-elections in 1992, fully 75% of voters followed party voting directions, resulting in plumping rates of 43% in one district (Gordon) and 63% in another (Kuring-gai). In the Kuring-gai case, less than 33% of electors filled in all squares on the ballot paper. In Queensland, plumping rates were 23% at the first OPV election in 1992. Since these rates are considerably smaller than the 72% rate of voters who wanted the option of plumping, we conclude that Australian voters wanted the ability to express maximum ignorance but apparently also want the ability to express maximum knowledge and presumably also would enjoy the ability to express intermediate levels of knowledge.

USA self-confessed ignorance levels: In 1958, constituents in congressional districts in which there was a Democrat v Republican contest going on admitted to knowing nothing about that race as follows:

A = have read or heard something about incumbent
B = have read or heard something about challenger
results:
    A & B: 24%
    A but not B: 25%
    B but not A: 5%
    neither (never read or heard anything about either one): 46%.

A majority of the US public in 1958 was unable to say which party had controlled congress for the last 2 years. [Data from W.E. Miller & D.E. Stokes: Constituency influence in Congress, Amer. Polit. Sci. Review 57,1 (March 1963) 45-56.]

Moving forward to 1988: 74% of the US public did not know the name and party of even one local congressional candidate.

A 1996 Washington Post/Harvard survey found that over 50% of Americans agreed with this statement: "Politics and government are so complicated that a person like me can't really understand what's going on." In particular only 26% knew the term of office of a U.S. senator was 6 years and less than half that a Congressman serves a 2-year term.

Conclusions: The rates of self-admitted ignorance ("heard and read nothing about either candidate") are large! Voter desire to have a voting system that allows expression of ignorance or indifference, is overwhelmingly large (72%) even if that voter is forced to express either total knowledge or maximal ignorance/indifference i.e. about all candidates except one, with no middle ground permitted. So for sure, voters by an overwhelming majority would want to have the "leave blank" option in range voting.

For math nerds: An argument about "unbiased estimators"

Suppose you roll 5000 (perhaps biased) dice and want to know what their total sum is. But you can only see 1000 of the dice; the other 4000 rolled under the couch.

• Method 1: assume the 5000 dice have the same average as the 1000 you can see. That is what statisticians call an "unbiased estimator."
• Method 2 (far worse): just sum the 1000 dice with no effort made to estimate the effects of the 4000 dice you cannot see. That is what statisticians call a "very biased estimator." Obviously, the unbiased estimator is going to be right a heck of a lot more often.

Refusing to have blanks, and thus forcing ignorant voters to guess, or to write "zero," results in a very biased estimate! The right way to estimate what voters ignorant about a candidate would have thought once they learned about him, is not to pretend they all would have thought "zero" or "a guess." The right way is to allow them not to express an opinion (if they so desire) in which case their vote is extrapolated from the voters who did vote and did choose to express an opinion about that voter.

Worried that totally-unknown candidates might get elected (thanks to blanks)?

Don't be. First of all, thanks to complaints about this issue, our current recommendation includes a "safety valve" rule on top of range voting that refuses to elect a candidate with less than 50% of the score sum of the sum-maximizing candidate, i.e, basically, candidates unknown to over 50% of the population cannot be elected (unless even the best knwon is virtually unknown so that we cannot avoid it).

Second, even without the safety valve rule, it would have been practically impossible anyhow, as we shall now argue, and also see this mathematical analysis.

Q. Suppose I get on the ballot, but I don't campaign and nobody has heard of me so they leave me unspecified. Suppose my friends and family give me a 99. Does that mean I get elected?

A. Without the safety-valve rule d: Yes it does! But, this is not a problem in practice, our polling studies in the real world conclusively show. That is because in practice, a lot of the people who might want to put "unspecified" actually put "zero." (By "a lot" I mean, a lot. Somewhere between 20 and 90% for sure. In our 7-candidate range election study, we received nearly 3 zero-scores, on average, per ballot. Zero was by far the most popular score to give a candidate, exceeding every other number's popularity by a factor of over 10, and with over 70% more zero-scores received than blank scores. Paper describing the study is #82 here.)

Due to this effect, there is a heavy built-in bias against little-known candidates. Range voting, by allowing blanks, merely reduces that bias, but does not come close to eliminating it. This is exactly the right thing to do.

So in any reasonably large range election where your friends & family voted for you but nobody else had ever heard of you, you can forget about winning.

However, if 50% of the population absolutely loved you and 50% had not heard of you, you might be able to get elected. I admit that seems implausible, but it does suffice to illustrate the beneficial bias-reducing effects we can get from this, which allow good candidates who are little-known, to get better vote totals. This would not allow them to win, but it would get them the attention they deserve for use in a future election.

Still Worried?

Q. I'm still worried about some "stealth candidate" getting elected via blanks. I'd like to give him zeros, not blanks.

A. Well, the thing is, there are a lot of conservative voters like you out there, and there always will be. Those voters can and will choose to intentionally put 0, where those of us who felt less conservative, would put blank. This leads to an enormous pit that stealth candidates have to climb out of.

Realistically, a stealth candidate loved by 5% of society and unknown to the rest, would get zeroed by at least 50% of the rest, leading to an average nonblank score for him of 9.4, placing him far in the rear. Check this probability calculation to estimate the chances your nightmare will come true.

If you want to worry about stealth candidates, you should worry about the plurality system, not range. Right now some wacko can often get elected, even though nobody knows a damn thing about him, simply because he managed, either through luck, apathy, or an inside deal, to get to be either the Democrat or Republican candidate. This in fact happens constantly with the election of, e.g, judges. (I recall an article in the Trenton Times [New Jersey] in about 2000 explaining how, if you wanted to be a Trenton judge, you should come up with $100,000 to contribute to the party boss, and then you'd get the nomination. This was standard procedure. Similar accusations – that Democratic-Party judgeship-nominations were for sale for $50,000 in Brooklyn – were recently made on the front page of the New York Post, etc.)

With range voting, the importance of the major parties and deal-making party "power brokers" will diminish and so I think that won't happen as much.

Also, I should add, if we eliminated the "leave blank" X-option, here are the bad things that would happen: The voters who would have wanted to put blanks, will be frustrated. There are a lot of them, and their desire to be honest, is being frustrated, and they don't like it. (I'm not just blowing smoke here. This all is based on my actual experience conducting a range election as a 2004 exit poll, paper #82 here.)

Also it won't work anyway, because those voters will simply award unknown candidates a score of 50, or whatever they think the average score is, or some intermediate value, or a guess, anyhow not zero. (Which in fact can lead to a lot more distortion and noise.)

An argument about why we need blanks somewhat related to (but also somewhat unrelated to) the abortion debate:

There is an analogy to the abortion debate. Recall: The "pro-choice" camp says we should be free to choose to have an abortion. The "anti-choice" (or "pro-life" as they prefer) camp says: nobody should get that choice because of an overriding moral imperative: They must choose "no abortion" because that is the only morally acceptable choice. Now in the present day USA and most of the democratic world, the pro-choice side is ahead in the polls and the law, but their opponents remain a substantial minority.

Fine. Now to return to range voting, the "pro-choice" camp would say: those who want blanks to be blank, can have that option. If they prefer blanks to be zeros, then we allow them to put 0s. If they prefer, say, 25s, put 25. It is your (the voter's) choice.

The "anti-choice" camp says "no. You do not get to choose. I insist you do it my way, which is zeros. Because I am definitely right, and everybody who says otherwise is definitely wrong."

But unlike in the abortion debate, here there is no moral imperative. In the range voting setting there is no reason to call the anti-choice side the "pro-life" side – since there is no pro-life issue here! In the range voting setting, they are simply "anti-choice"! So I do not see the rationale for demanding blanks be zeros and for insisting on the God-given rightness of only this choice. I see a rationale for letting voters choose what they want, and if they want to express "no opinion" by putting an X (intentional blank score) I say let them.

Two other arguments for why blanks are a good thing to have

Having Xs totally prevents problems arising from the too-many choices paradox.

Also, there is justification found in the bible (see the quote from Samuel) for preferring the Xs=blanks option.

How it looks from the candidate view instead of the voter view

Put the shoe on the other foot, I say to those who want blanks automatically to be scored as 0s. (An old principle for judges: try to see it from both sides of the case.)

Suppose you were the candidate about whom I am ignorant. (Or, more likely, you are just a random person about whom I am ignorant.) Would you want me to say to you "I have never heard of you. Therefore, I will automatically assume that you are exactly on par with Adolf Hitler, I intend to give you zero score and pay absolutely no credence to anything you ever say. Simply because I have not heard of you before."

Well, I suggest to you, that you might not appreciate me taking that view. [But oddly, those in the "blanks must be automatically converted to zeros" school seem to have no problem taking the same view...]

I think you would prefer it if I instead take the initial view that you are probably an average person, not a Hitler, and I will assume that until proven otherwise. In fact, more precisely, I will take the view that my opinion of you is the same as the average opinion of the people who do know you – until proven otherwise. This is exactly what the "blanks" option in range voting accomplishes.

But the blanks option in no way prevents those who do prefer zeros, or 25s, or whatever, from exercising that preference. Unlike the must-be-zero-camp, which truly does want to prevent the blanks camp from exercising their preference.

How it looks if we get rid of blanks:

If you do range-vote exit polling as I have, then it quickly becomes apparent to you that many US voters do not know, and say right to your face they do not know, anything about various candidates, and they say right to your face they want to leave those slots blank for that reason.

Now you as the pollster then have two choices. You can tell them they are negligent irresponsible jerks and tell them it is absolutely ridiculous that they are voting in any election, and you want nothing whatever to do with them. Oh, and if you do vote, you irresponsible jerk, then I insist you fill in that slot with your total guess. Or, you can tell them, ok, fine. Please leave the slot blank.

Which approach seems more likely to yield better results for society? Not to mention, which approach seems more likely to gain more support for voting reform?

Another problem is those people actually may not actually be irresponsible jerks. For example, I challenge you to find out data about judges (there are many USA elections for judges). It is hard. Usually you cannot. Only a fairly small fraction of society (e.g. those who have been in his courtroom) really have much of a clue how good that judge is. So there you are, a voter, participating in a 10-choice election for a judgeship. You heard judge A recently took bribes and is an alcoholic running from jail. OK, vote zero for him. You heard judge B sounds pretty bad but not as bad as judge A. Give him 30 out of a possible 99. OK, there are 8 judge-candidates left you know nothing about. What do you do? Leaving their scores blank could be a good idea. Giving them all zero is definitely a bad idea. Seems to us that many voters, in that situation, want the opportunity to say what they do know about the judges A&B they do know something about, and say nothing about the judges they know nothing about. What good does it do to deny them their desire?

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