Forest said (extracted from complete original message below): >> Constraints tend to limit the information efficiency of >> the ballot.
Here's another way of looking at the efficiency of the ballot. We don't want it to become too efficient because ballots are very poor storage media. Or put differently, an election in the abstract (or in ATM-style voting machines) can afford to ignore some of the mechanical considerations that cause problems in elections. I've worked at the polls quite a few times, and I've always found it to provide a different perspective on the notion of voting. Most of that has been a shift in attitude, and hardly something that would interest a group concerned with election methods. But this time I also worked at the election board, processing absentee ballots (most of the ballots in the area where I live are absentee), and there I discovered some things that might bear directly on the choice of election method. While we look at the minutiae of mathematical criteria and the influence of imperfect voters, and possibly even consider software requirements, we tend to disregard such mechanical problems as feeding paper ballots through a counter, and reading imperfectly marked ballots (that bizarre -- and avoidable -- Florida chad problem notwithstanding). Here, in this part of Washington (Washington state -- it was originally going to be called "Columbia", but it was thought that might be confused with "District of Columbia") we use optical scanners. One marks a choice by connecting the two ends of an arrow, so a valid mark is a line between two fairly small points on the ballot. Obviously, the ballots have to be of good quality. They are light card stock, with matte coating. A quick look at the machines shows that they use lasers. There appear to be four lasers across, at the point where the scanning actually occurs. I think that means that the marks must be restricted to four zones that run the length of the ballot (top to bottom). You can see how this would complicate the use of any ranking method, in which the candidates would be listed vertically, with a whole 2D array of boxes next to them. It would seem that the machines we were using couldn't handle that arrangement. I don't know what they use in Australia or Ireland to count ballots, or in other places that use rankings. But the mechanical cost would seem to depend on the choice of method, with rankings being more expensive. Just conjecture; I haven't looked into this. One problem we had to deal with was possible read errors caused by spurious marks. There might be a pencil spot, or an incomplete erasure. In general, marks, even faint marks or smudges that obviously weren't votes were assumed to be a problem, and the ballots had to be duplicated. Duplicating a ballot is an involved process; an identically marked ballot has to be created, and you can imagine the amount of procedural safeguard that is required. For example, possession of pencils is limited to pairs of workers; if you get up and leave your partner at the table with ballots, you take the pencil with you. So duplication is a slow and costly business. And there are other similar processes, such as examining ballots for possible problems, that are also time-consuming. Note that (1) Only smudges within an area where a line would be a valid mark (a bit on the ballot, ignoring for now the fact that only certain patterns of marks are valid) are problems, so the number of places where such smudges might occur -- and hence the number of problem marks -- can be expected to be roughly proportional to the complexity (number of bits). Often, the smudges are caused by a pencil mark offsetting from one part of the ballot to another because the ballots are folded. (2) These offset marks could be expected to occur on the order of the square of complexity. Clearly, more complex ballots are going to demand more duplicating, and the work of duplicating a single ballot increases with complexity, so total duplicating work will be roughly o(complexity^3). Something to consider when choosing between a ranked election method that uses arrays, and something like plurality, approval or cumulative that requires only a single bit per candidate. Another consideration is: Remember earlier discussions of the usefulness of a "None of the above" option? This was mostly considered in terms of how to take into account that voters are displeased with the choices, but there's another way to look at it. When checking ballots, we would sometimes see a smudge that almost certainly was spurious, perhaps caused by the opposite side of the ballot picking up ink off a newspaper or some such. Sometimes, that would be the only mark for a group of candidates, and would have been a valid vote if it were real, but in bad cases, it can be hard to tell if it's a vote or not. And sometimes there was a clear vote, so the smudge could only be spurious. The difference in the two cases was that in the latter, any spurious mark must produce an invalid ballot, while in the former, the Hamming distance between valid ballots is one, so there is no possibility of error checking. In that case, a "None of the above" option would guarantee a Hamming distance of two, so any single error raises a flag. I realize it's unrealistic to expect voters to compute cyclic redundancy characters, but it should be possible to design a system that would provide rudimentary parity checking. IRV, or any complete ranking, would do that automatically as long as all candidates must be ranked. Plurality does not. Even if voters were required to make exactly one mark (rather than zero) or their votes won't count, how we know what to make of a single faint mark? Is it a vote, or is in an invalid ballot (no marks) with a smudge? Approval could be made to comply with the simplest error checking by requiring a valid ballot to have "yes" or "no" marked for every candidate. I suppose Plurality would also comply under the same requirement. However, we could expect the inevitable confusion as voters find themselves faced with a task that can only be reliably carried out by a pigeon after substantial training. I think that the incredibly poor mechanical qualities of paper ballots need to be considered in any evaluation of election methods. To a rough approximation, it seems that the more efficient the ballot, in the information-theoretic sense, the less reliable it is going to be; sophisticated error checking and correction are going to be hard to incorporate into paper ballots. Therefore, from a practical perspective, perhaps it would be better, once again, to give preference to methods that make it easy to identify errors. By the way, I ran across the inevitable votes for the Mouse and Duck, and it occured to me that people really do want the ability to vote "None of the above", whether it has any effect on the outcome or not. Perhaps voting for Mickey Mouse really does serve a purpose, and he should be entered in every contest; he seems to have an important role to play in world politics. >> From: Forest Simmons <[EMAIL PROTECTED]> >> Subject: [EM] Advantages of CR style ballots >> Joe Weinstein argues the advantages of unconstrained CR >> style ballots below. I would like to add my two bits >> worth. >> Most of the arguments against the use of CR ballots are >> based on the misguided assumption that the only way to use >> CR ballots is to give the win to the candidate with the >> highest average rating. >> That assumption is tantamount to believing that the only >> way to use ranked ballots is to give the win to the >> candidate with the highest average rank (the Borda >> winner). >> Note that CR ballots can be used for head-to-head >> comparisons (generalizing Condorcet methods). >> CR ballots can be used to find the candidate with the >> highest median rating (generalizing Bucklin). >> There are many other uses of CR ballots. Lorrie Cranor >> uses CR ballots as input for her Declared Strategy Voting >> (DSV) methods. >> All of these uses of unconstrained CR ballots allow the >> voter more freedom of expression than the constrained >> methods that use the same information capacity ballot. >> Constraints tend to limit the information efficiency of >> the ballot. >> For example, the lone mark plurality ballot can be used >> for Approval if the constraint is removed. >> Another example: >> Three bits of information are required to distinguish >> among five candidates, so a ballot that allows the voter >> to rank five candidates requires making at least a three >> bit mark beside each candidate's name. Without the >> constraint, the same ballot could be used to rate each >> candidate on a scale of zero through seven. >> More commonly five bit codes are used to rank five >> candidates (five distinct bubbles to the right of each >> candidate). The same ballot could be used to rate each >> candidate on a scale of zero to 31. >> Furthermore, the lack of constraint makes it harder for a >> voter to foul the ballot. In other words, a voter can >> hardly violate non-existent constraints. Which is harder >> to mess up ... lone mark or Approval? A lone mark voter >> who doesn't notice the (rather ridiculous) "one mark only" >> instruction can accidently foul his ballot if he likes two >> of the candidates. >> Forest
