A rumination on why I think “democracy” has to mean more than “majority rules” or “the favorite wins”—even when only a single candidate or proposal is being chosen.
The possibility of Condorcet “cycles” infecting the preference-rankings of groups is pretty well known by now—especially since Arrow’s impossibility theorem. The idea is that a group entirely composed of individuals whose preference-rankings are transitive may end up liking (as a group) A more than B, B more than C, and C more than A. This can happen because different sub-groups make up the three aggregate ratings. This (and other voting paradoxes even involving pairwise comparisons and Borda counts) have led some observers to denounce majoritarianism. Such critics consider it either an approach that can’t provide unambiguous winners when there are more than two choices, or worse, something that unambiguously provides the wrong answer.
Now, as I look at these matters, there are at least two essential characteristics of fair democratic choosings. First, they are egalitarian in this way: they must, to use the old Benthamite language, “count each vote as one and none as more than one.” That is, they cannot countenance weightings of most kinds, whether they are considered to follow from any rankings (cardinal or ordinal) of the voters or from any external assessments regarding the value of this or that vote or voter. Second, they are egalitarian in another way: the authority granted winners of elections must, in some rational manner, reflect ratios involving both the number of eligible voters and number of votes received. (I will not take up this latter requirement in this OP.)
While simple majoritarianism seems to share both of those desiderata, I take it that the latter (my own view) can’t rightly be characterized as a majoritarian position itself because it does not accept what is commonly known as “the majority criterion.” What is that? It simply requires that If there exists a majority that ranks a single candidate higher than all other candidates, that highest-rated candidate must win. As will be seen, there are good reasons for those with sound democratic principles not to join with majoritarians on this matter. In any case, the (let’s call it) “Egalitarian Proportional Democracy” I’m pushing for here shares with majoritarians the views that political actions and offices must be taken and distributed on the basis of the number of voters who want or don’t want something, rather than on how much they want them (as well as on the other matter that I’m not planning to discuss here). But surely that doesn’t tell us very much. Can at least the egalitarian portion of my description of Egalitarian Proportional Democracy be fleshed out? Let me try.
Suppose eight people are having a party and are trying to decide what soda to bring. [Based on an FMM comment, I add here the assumption that, for whatever reason, it would be a major hassle for there to be more than one choice of soda at the party.] And let there be four possible choices: Cola, Lemon-Lime, Orange and Root Beer. There’s no unanimity among the revelers, so, being the good (small-d) democrats they are, they think that the majority ought to have its way and plan a vote to decide the matter. Here is the result when they are asked to give their favorite (here designated with ‘X’):
A B C D E F G H
Cola X X X
L-L X X
Orange X X
RB X
As can be seen, while Cola receives a plurality of the vote, no flavor gets a majority. One member therefore suggests a run-off with the first and tied-for-second contenders only, leaving off RB all together since it did so poorly. Here are the results of this run-off election (with ‘A’ indicating an abstention):
A B C D E F G H
C X X X A
L-L X X A
O X X A
This vote didn’t help: there has been no movement at all because voter H absolutely loathes all the flavors except RB and refuses to pick any of the others as a passable choice for the party.
The revelers aren’t completely stuck though, because there are other voting possibilities. Let us suppose that, like me, this group has no truck whatever with the inter-personal assessments of preference intensities required for cardinal ordering, and that they are also skeptical of ordinal rankings to the extent that those assume similar “distances” between preferences. They think, that is, that there could be a huge divide between one person’s 1st and 2nd choices, and hardly any at all between another ranker’s 1st and 2nd picks.
Fortunately, two members of this group have been regularly assaulted by emails from voting reform organizations: one, from a group that pushes Approval Voting (“AV”), and another that favors Score Voting (“SC”). Those two discuss the matter with the other six party planners and the SC advocate is able to convince everyone that they can exclude all the questionable preference weights by using the following scale:
FAVORITE……………………………………………………………………4 PTS
GOOD ENOUGH (WOULD DRINK IT IF AVAILABLE)………………….3 PTS
PASSABLE (NEVER HAD BUT WD TRY IT IN A PINCH)……………..2 PTS
NOT OK (NEVER HAD & WON’T TRY EVEN IF THIRSTY)…………..1 PTS
REALLY DISLIKE………………………………………………………….. 0 PTS
The AV supporter is on board with undertaking a new vote that would use this scale, but only if the assignments of 4, 3, or 2 points are counted as “Approvals”—meaning that the voter can “live with” the choice. This is agreed upon as well, and the third vote is taken. For ease of counting, I represent the approvals here with an “(A)”:
A B C D E F G H TOT. Apps
C 4(A) 4(A) 4(A) 2(A) 2(A) 1 0 0 17 5
L-L 2(A) 2(A) 2(A) 4(A) 4(A) 2(A) 2(A) 0 18 7
O 3(A) 2(A) 0 3(A) 3(A) 4(A) 4(A) 0 19 6
RB 3(A) 0 0 0 1 3(A) 2(A) 4(A) 13 4
As can be seen, while the Plurality victor was Cola, the SC winner is Orange and the AV winner is L-L!
Perhaps it will seem that this embarrassment of “winners” is the result of the weirdness of there being so many “never tried it” votes with respect to what seem like common carbonated drinks. But it is important to realize that an attitude of “I really don’t know much about her (or it).…” toward political a political candidate or proposal isn’t unusual at all. Look at the results above again, but this time, think of it as a political election for a representative, with each coming from a different Party. (Perhaps replace “Cola” with “Corporatist”; “L-L” with “Liberal”; “Orange” with “Outsider” and “RB” with “Republican”.) This may make it clearer that there can be a large number of decisions in which the assignment of one or two points (approval or disapproval) will largely be a function of the varying amounts of risk that voters are willing to take. Some people will be OK with this or that relatively unknown candidate or proposal; others will not be willing to take any chances.
Keeping all this in mind, which “winner” will the authentic egalitarian support in this election? The Corporatist, because he is the favorite of the largest number of voters? The Outsider, who got the highest score? Or the Liberal, who most voters found to be minimally acceptable? In my view it is the number of approving voters that the sensible democrat must take to matter most. Just as we ought not to be stuck at parties with nothing we can stand to drink, we ought not to be stuck with ruler/representative A when more people among us can stand candidate B. On this view, if it is to be used to determine what “the people” do or don’t want, majoritarian/egalitarian-style aggregation should be understood as the counting of approvals, where each person’s approval is given the same weight as everyone else’s, regardless of how enthusiastic or tepid it is. That tack definitely seems more conducive to stable regimes than one in which candidates that a ton of the populace don’t approve of get to take office.
That is my current take on the matter. I recognize that I have here avoided all of the complicated issues surrounding strategic voting and how that is likely to affect results (if you’re curious, see the Wikipedia article on “Approval Voting.”) Anyhow, I look forward to comments to get a better handle on this. Thanks.
I’m a federalist. I think it’s better if each table gets together and picks their favorite drink.
They can work out a consensus better in a very small group as friends taking into account strong preferences and or dislikes
There is no reason that the entire party must drink the same thing.
Peace
I’ll admit that I only skimmed through your post.
There are mathematical proofs out there, showing that a perfect voting system isn’t actually possible.
Personally, I like the Australian system (maybe because that’s where I grew up). They use preferential voting, and voting is compulsory. And I think both of those help. And yes, I’m sure that people can point to Australian elections where things went badly.
I remember several years ago, I was in a mathematics department. And the department decided to try out preferential voting. They didn’t like the result, so they switched back to plurality voting. This was voting for the department executive committee.
Here’s my observation about that. With preferential voting, the people elected were mainly those well respected as fair minded moderates and with good overall judgment. But they were not the department members who were considered to be the stars (department celebrities).
I guess they preferred the star system.
fifthmonarchyman,
Well, I like deliberation, etc.where possible, too. But most countries in the world are much too big for town meeting style government. And here in the US, every state is too big and a ton of cities and towns are too big.
A lot of people say that our Congress is much too small given the number of people in the US. They claim that it’s effective disenfranchisement to have one rep per so many thousand people. I don’t agree with that myself, but the point is that if you jack the number of members of Congress by much, you won’t even be able to have effective discussion there (assuming you can now)–never mind among the general populace.
Thanks, Neil. Two questions: can you explain what the rules were to the “preferential voting” system you refer to? And what are the properties of a “perfect voting system” that were mathematically proven to be impossible? I.e., do you mean Arrow’s impossibility theorem or something else? If something else, can you describe what it is that’s supposed to be impossible? Thanks.
It’s sometimes called the “single transferable vote”.
A voter gives preferences to each candidate.
The rules are a bit complex. But the basic idea is that you eliminate the candidate with the fewest votes. Any vote for this candidate is now transferred to the next preference.
A perfect system is one which could never give anomalous results.
Fascinating topic.
A few weeks back, I read an entertaining blog piece regarding the quandry regarding Brexit and three-way voting…
Personally, I am a fan of Single Transferable Vote, because it does actually honor egalitarianism, but it obviously only works where you have multiple “winners”…
The USA has a mindblowingly large departure from equality, but that was intentional, or so I’ve been told…
Yes–when I complain about the lapses of democracy here, fifty libertarians chirp, ‘that’s not a bug, it’s a feature!’ Re: STV (or the Hare method), I’m familiar, but, for various reasons, actually prefer SNTV, (where everyone gets to vote for one favorite only in a multi-member district). It too provides for minority representation, and was used for years in Japan, but has been derided as the worst system in the world (and even as the cause of a war). I have a draft of a paper in which I try to rehab sntv.
Neil Rickert,
What makes a voting result ‘anomalous’ according to this proof?
Does it all even out over time? That is, if my candidate gets screwed one time, it’s just as likely that the next time my candidate will get the benefit?
Unless of course the two parties become so polarized that voters refuse to split tickets or change from election to election?
But that would never happen would it?
Never mind. 😟
Voting systems is a big area of mathematical inquiry, and it can be shown that there is no perfect system. A mathematician I know worked on that, and one day his department had to form a committee. He proposed a preference system, and they accepted it and voted for committee members. Then they were unhappy with the result, so he proposed another system, and they used it and got a completely different list of committee members. Then he proposed another system, and again they voted and again got a very different list of committee members. They ended up thoroughly pissed off at him.
There was a series of articles on voting, I think in Mathematics Monthly. But it was more than 25 years ago, so my memory of the details is a bit hazy.
The basic idea of an anomaly, is when the winner of the election has less support than one or more of the losers.
Democracy has never worked ever because it allowed a very small group of people, who call themselves scientists, to enforce and ideology up on all the rest replacing one religion with another… I will not name names because everyone here, other than Byers, knows what I’m talking about…
Well, I’m concocting my own system. With any luck, a lot of people will someday be pissed off at me too. (Or at least have another reason to be.)
I’m not sure what a perfect voting system would be, apriori. There are different goals that one can highlight. Sometimes you can’t meet them all, or meet them all efficiently. But, for example, you can ask yourself, given the constraints and preferences of the partygoers in my example, what soda should be purchased. Not everyone will agree with you, but that’s sort of the nature of the beast when there’s no unanimity.
That seems to be the majority criterion I mentioned in the OP. I think it’s pretty easy to set up a system that meets that–but only if there are no other axioms.
Add me. So, me and Byers.
I think that when a body gets too big for effective consensus building the solution is to split it up into smaller parts.
A while ago you asked about Protestant politics.
Well that is the congregational side of things. A church fights over something and when no consensus is available and the issue is important two new churches are born.
They will probably maitain some relationship with each other and they will probably cooperate on issues deemed to big for individual congregations to tackle.
Sometimes a group will stray too far from “orthodoxy” and they will no longer be deemed to be a valid “body politic” by the rest of congregations.
I really see no reason why this couldn’t work in secular government as well. I think something vaguely similar held sway in this country till probably FDR.
You will loose a little bit in efficiency but efficient government is a recipe for eventual tyranny.
peace
Congrats walto!
Welcome back! I hope you and you know who, get along…agian…
You still need to have a way to aggregate the parts you’ve split the total populace into. So, for example, even if one is a confirmed Federalist, we can argue today about the method of selecting a US President based on the current Electoral College system, or, if not, how that system ought to be revised. The more more divided the system is, the more likely it is to fall apart completely–however nice the little city-states might be. And today’s world is not very similar to the world of the early levelers.
Still don’t know what you’re talking about.
There is always the probability that representatives, once elected by any method, will change the method to favor themselves.
There is also the observed phenomenon that regardless of the system, candidates will find a way to position themselves to have a shot at winning.
As evidence, I note that elections are remarkably close these days. The state of Virginia had a tie vote for state office, which was decided by a coin toss.
Hillary’s quest for her party’s nomination included six coin tosses, all of which she won.
keiths
I think that the Electoral College system is probably the smartest political idea since the ballot box.
It keeps the more populated areas from running rough shod over the rest. It’s definitely not perfect but it forces candidates to pay attention to the wishes of all of the country and not those of a chosen constituency.
I agree but I don’t think that is always a bad thing. It makes you choose your battles wisely and Russia and several small countries is a lot better for the world than the Soviet Union.
peace
Indeed. I have some thoughts about that too.
I think my ability to think about strategic or insincere voting (as well as that sort of “positioning” if it’s not the same thing) is limited. It gets too abstract for me. I think you’re right that that’s ant that that’s an important disability of mine. Ideally, I’d have a co-author who is good that that sort of stuff, but my relative isolation makes such joint ventures more difficult.
I’m well aware of that position, but, obviously, a lot of people disagree with it.. It makes everything of geography and much less of population. Some votes are worth thousands of others. That seems terribly unfair to some observers that voter A has so much more influence over the election than voter B, simply because of where he or she lives.
Would it have been better for the world if the US had split in two?
Aha. Finally got it. Thanks.
I suppose it would depend on the nature of the split. It’s definitely better that the south lost the civil war.
But I’ll bet that there are times that New England would be happy to have the same relationship to Texas as it does with Canada and I’m sure that Texas feels the same way. 😉
A much better scenario would be that the laws passed in Washington DC would leave the residents of these very different states to handle their own affairs as much as possible.
peace
It really depends on what you think the ideal job of the president is. I don’t think it’s about making sure that every individual person gets their fair share.
I think it’s about making sure the various states don’t take advantage of each other and that our collective interests are advanced internationally . Or at least it should be
peace
What “New England thinks” or “Texas thinks” about secession have to be decided somehow. Your couple dozen church congregations are not going to be able to decide that during tea and cookies.
What “the job of the President is” means either what is set forth in the Constitution and interpreted by SCOTUS or what the voters want the job to be or some combination of those. To determine what the voters want the job to be requires counting them and their votes. Otherwise we don’t have a democracy. There are different views about what constitute fair ways to determine what “the people” want. I get that you have particular views on this (although you don’t seem to have much to say in support of them–at least so far). But what I’m trying to get across to you at present, is that there are other view than yours about the fair methods of determination. What you think the President’s job is “about” is really neither here nor there.
I don’t want to get too partisan political here but a crass argument can be made that the present immigration question is really about the residents of the smaller states being concerned about the more populated states unfairly trying to overwhelm them politically.
New Immigrants are more likely to end up in cities but at the same time natural born inhabitants of cities tend to have a lower birth rate than more rural areas. So politically it makes sense for urban areas to promote immigration and for rural areas to resist.
I’m not saying that this is anyone’s conscious plan I’m just saying the Electoral college is a great remedy for schemes or supposed schemes like that.
peace
Yes, and there is a process to amend the constitution if you choose. It’s definitely weighted so that it’s hard for the majority to impose it’s will on the minority.
Peace
Interesting.
Right, but if you want to amend the Constitution, it’s good to have to have an idea of how you think it should be written, of what would be better. I’m getting the picture that you like it as is. I personally think it’s a mess. So it offends my sense of fairness, of what it means for the people have power, while it seems OK to you. But that’s fine: that kind disagreement is part of political life.
He has changed… for better… You will see… 🙂
No I think it’s a mess too but think that most ideas for improvement end up making things worse.
Peace
Its not about votes but about the contract of men who are free on how they rule themselves.
If the contract includes a democratically elected this/that then it means every man gets to choose who rules the group. since there are so many men then it must be a head count. simple.
Anything else is saying the man has more/less right to choose who rules.
This is why the concept of a minority prevailing in elections is against the very idea of a free people. Just like in the election of Trump over Clinton, I understand she got more votes. YES it would be more evil if she won but thats not the point.
This also includes the demand that if one does not want to vote then you can so choose.
its about original presumptions of free men deciding on who rules them.
anything other then majority will imposition is immoral and illegal from presumptions of freedom except in settled conclusions like constitutions.
Again I’m a federalist
I think that power should be decentralized as much as possible. We got away from that idea about 80 years ago. It’d be a good idea to get back to it.
Peace
I’m on board with a lot of that, Robert. You and I may not agree on too much, but we’re obviously both (small “d”) democrats!
Four suggestions:
1. Abolish all “upper houses”, they are inherently undemocratic. In my country, the largest state has 12 times the population of the smallest, but both elect the same number of Senators. The result is permanent pork-barreling and a permanent loonie fringe in parliament. In one case, a Senator won his seat despite receiving only 0.5 per cent of the total votes cast (for a sense of scale, you would need a quota of around 300,000 votes for your party’s slate to get elected in the normal way).
2. Only elected members of parliament are eligible to undertake executive positions, including the head of state
3. Abolish intermediate levels of government. Get rid of the states and provinces, which are largely reflections of 19th Century modes of government and communication. Local assemblies of a suitable size, and a single-chamber national parliament elected on universal suffrage.
4. Publicly fund election spending, with allocations proportionate to a party’s popular vote
De localizing government is analogous to having monocultures in agriculture.
Highly efficient, but susceptible to total population death.
I agree with a lot of that, too, timothy. (I don’t think FMM will find your anti-federalism very congenial, though: you too should go a few rounds on that issue here! Tell us why you don’t like decentralization!)
There is only one unicameral legislature among the the states here, in Nebraska. Paine and some other radicals got one established for a few years in Pennsylvania, but James Wilson and some other moneyed “Founding Fathers” got their Senate back in pretty short shrift. A group of Progressives in Oregon (called “People’s Power” I think) were close to getting rid of their Senate on a couple of occasions back in the Teddy Roosevelt days, but they couldn’t quite pull it off. There may be some sense in having a mechanism to slow bills down, but an “upper branch” isn’t needed for that.
That’s a nice metaphor. Would you care to flesh it out a bit?
Why do we have anti-trust laws? My take is that monopolies rise because they provide some desired service or commodity, but eventually become exploitive.
Kings and dictators are efficient, but no longer popular. Why?
I think all positions of power eventually become corrupted, because there is a natural ratchet. You can have a well managed and benevolent government, but eventually, a bad person or two gains a foothold. Almost by definition, they will take steps to maintain their power. They will hire and promote loyal subordinates.
It may take time, but eventually the entire system is corrupt. Those of us wo are not Catholics can see the church’s failure to prevent child abuse or to remove abusive priests. The same phenomenon has recently been exposed in the Southern Baptist church. I am not the least bit surprised, because I worked in protective services.
This phenomenon can be generalized. There is no magic way to prevent corruption.
But it makes no sense to put all your eggs in one basket. The smaller the unit of power, the easier it is to fumigate.
I realize this is a sloppy presentation. But people would be wise to read about the history of democracy
The Wikipedia article on Athenian democracy might be a place to start – people power – unless you were a slave or a woman.
Lots of issues. Who defines boundaries? Who decides method of polling, voter registration, candidate eligibility, oversight and enforcement of rules…
Regarding a fair polling system, I vaguely recall listening to a radio programme discussing options and a half-serious model of transparent voting where all preferences could be seen in real time and could be changed. Imagine a large open space containing all candidates, (issued with a box to stand on) and all voters. You vote by standing next to your preferred candidate. But you can change your mind on seeing where others are standing.
Another method for getting your way is to buy the election and then stuff the judiciary with cronies.
Single transferable vote is fairer than gerrymandered boundaries with simple majority rules. Better when combined with ease of voting making required voting acceptable. Why not on line voting? Why not a real time output of votes cast?
Why does an experiment in democracy often result in military dictatorship? Who guards the guards?
Questions! So easy to ask… 😕
Interesting.
We are subject to a spectacular abuse of democracy at the moment – as I’m sure you’re aware. In a simplistic referendum in 2016, the entire group of UK nations was pooled and asked the question ‘Leave’ (the EU) or ‘Remain’, with a 50% threshold for implementation. The turnout was 34 million, the excess for Leave 51.9% – a swing of just 700,000 would wipe it out.
Many consider it ‘the greatest democratic exercise the country has ever undertaken’. Guess which side they are on? Our own PM has averred that failure to implement would be ‘a gross betrayal of democracy’. The same line is taken against proposals to put it back to the people, which is quite a spectacular logical contortion straight out of Orwell. Scotland and Northern Ireland were firmly for Remain, but outvoted by the numerical superiority of England and Wales. They aren’t happy, giving hope to separatists. The icing on the cake is that the Unionist DUP, a NI pro-Brexit anti-reunification party with 10 MPs, holds the balance of power in Parliament.
With 40 odd days to go, we still don’t even know what kind of ‘Leave’ we are going to get. Because the ballot was silent on that matter, it is often assumed that a vote for Leave was a vote for any of them, while everyone insists that the ‘17.4 million’ all wanted the same version as they. Our representatives nearly all insist that the referendum must be ‘respected’. Some people go so far as to argue that any parliamentarians opposing this should be deselected – a very uncomfortable position to my mind, starkly illustrating the tyranny of the majority. There are death threats, and dark warnings of civil unrest.
And so, however unsatisfactory the actual outcome is to either side, we must implement some version of Leave. We are paralysed by this. Consider it a cautionary tale: How Not To Do Democracy.
In a referendum, there is no candidate – someone else has to deliver on promises made; people can say what they like. So there, more than anywhere, questions on ballots need careful design, and thresholds set to guard against deep division on close votes. If ever there was a question that should not have been a simplistic 50% binary …