Voting Systems: Ballots, Their Counts, Biases, and Contexts.
Summary
Ballots express preferences. Preferences are psychological rather
than logical, and complex rather than linear. Ballots can be
applied and counted different ways to achieve different purposes.
Ballots are like tools -- each kind of ballot has a bias or
"mechanical advantage" that produces predictable results. The
results are successful within appropriate contexts. Pick the right
tool, use it the right way and in the right context, and you
achieve your purpose.
Introduction
There are dozens of kinds of ballots and voting systems. A
discussion of them all would result in a very large and very dry
book. I shall try to be brief here, and touch only on the most
important fundamental ideas and ballots mentioned in the
submissions. The cursory style of this submission (albeit long) may
have a choppy and disconnected result. I must rely on the reader to
connect the dots.
Preferences
Although we could have random ballots (flip a coin), delegated
ballots (choose for me), and proxy ballots (choose #3 for me), the
kind of ballots at issue here are "preference" ballots -- ballots
designed to facilitate the expression of the voter's
preference(s).
It is important to understand the nature of preferences and how
they work. Preferences are psychological, have an emotional
component, summarize a complex situation, and have little to do
with linear logic. Preferences are global decisions based on
changeable and changing combinations, permutations, and weights of
criteria.
For example, I prefer apples to bananas for texture; bananas to
cherries for craving (potassium); and cherries to apples for
flavour. A is better than B; B is better than C; and C is better
than A. Am I illogical or confused? Certainly not. I was not
literally weighing the fruit, nor measuring any other simple linear
dimension, where A would have to be better (heavier) than C.
Preferences summarize all the qualities of each alternative and
come up with the qualities that "tip the scale".
Also, it is important to note that the nature of preferences based
on pairwise comparisons is different from the nature of preferences
articulated by ranked rosters of successive preferences. The kinds
of comparing are different. Pairwise comparisons are isolated,
simple comparisons which logically admit ties because of that
isolation. Successive preferences, articulated on ranked rosters,
are integrated complex comparisons which explicitly preclude ties
in order to increase the probability of a clearly ranked cumulative
result.
For example, when pressed to rank the fruits, I prefer bananas over
cherries, and cherries over apples. But my preferences rotate
(cravings shift), and the weights of the reasons change.
Preferences are dynamic, not static. The election results you get
next month will not be identical to the results you get this
month.
Consider the following alternatives: Tea Party, Cocktail Party,
Loud Party, Wild Party, Garden Party. You can think of these
alternatives as plans of action, political parties, candidates,
whatever. The principles involved are the same. Let's say that the
order of the Parties above is the outcome of holding a first
preference (FPTP) ballot. This result, like pairwise, is an
isolated comparison. The first preference ballot asks the voter,
"Which alternative is your favourite?" It does NOT ask the voter,
"How would you rank these alternatives?" Consequently, the order of
the Parties above is NOT the rank of those Parties. In fact, the
Garden Party might be "everyone's second choice", that is, the
second choice of the majority of voters.
In order to find out the ranks of the Parties we have to employ a
ranked roster of successive preferences. These ranks will be
legitimate, integrated complex comparisons. The outcome might be
Tea Party, Garden Party, Cocktail Party, Wild Party, Loud Party. On
occasion the integrated ranks may mirror the order of isolated
comparison, but that would be largely coincidental.
When we collect all the ballots of successively ranked preferences,
we count them. We could just add up the ranks each alternative
received. Like golf, the winner would be the alternative with the
lowest total. The first runnerup would have the next lowest total,
etc. Alternatively we could use a Borda count which assigns points
in the exact reverse of the available ranks. For example, in a
field of five alternatives, a rank of 1 is worth five points, 2 is
worth four points, etc. The result is exactly the same. Borda is
just more "intuitive" in that the winner gets the most points.
After ranking all the alternatives, and totalling all the ranks,
the roster ballot answers the question, "Which alternative would we
choose next, if we cannot have our favourite?" This is a summative
rank of integrated preferences that gives us the Best Compromise
alternative. The Best Compromise can also be thought of as the
"least offensive" alternative, or the alternative that provides
"the least dissatisfaction to the greatest number". Counting a
ranked roster of integrated preferences will always result in the
Best Compromise alternative even where the count does not choose
the alternative with the greatest first preference plurality. [On
the CA website go to Learning Resources-Other Links-The Keele
Guide-PR Squared-Various nonintuitive features of electoral
systems. Also Google to The Mathematics of Voting website to see a
clear and simple demonstration of how counting systems affect the
outcome of a ballot.]
To find the alternative with the greatest plurality, we must count
the first preferences in isolation. This is mathematically
identical to the familiar FPTP ballot. You can think of a ranked
roster ballot as an expanded first preference (FPTP) ballot, or a
kind of "drop down menu" if you like.
In any case, the winner amongst first preferences is the Most
Favourite alternative, or the "most pleasing", or the alternative
that provides "the greatest satisfaction to the greatest number".
So now we have the Most Favourite alternative and the Best
Compromise alternative. How do we choose between them? Well, we
could have a run-off election, which is an expensive and drawn out
procedure. Or we could set a threshold of popular vote that the
Most Favourite must meet, or else the Best Compromise count will
proceed. So, how much more important is the Most Favourite over the
Best compromise? Or, what is the maximum percentage of voters you
can leave relatively dissatisfied? My personal intuition says that
the Most Favourite alternative is about twice as important as the
Best Compromise. So a vote for the Most Favourite is twice as
valuable as a vote for all the other alternatives. It follows that
the threshold of popular vote for the Most Favourite would be
one-third plus one vote. That would leave about two-thirds of the
electorate relatively unsatisfied. Although two-thirds sounds high
for disaffection, one-third sounds high as an achievement.
In any case, this system of a ranked roster ballot, counting the
Most Favourite first, and the Best Compromise if necessary, at the
riding level, would be the single simplest thing you could do to
fundamentally alter the politics of BC. You would not have to
change anything else in the electoral system. Wasted votes
(illegitimacy) and warped results (unfairness) would both be
minimized. There would likely be an incidental or accidental
increase in proportionality as well. Though, this change in ballot
is not specifically nor necessarily a proportional representation
measure. There would probably be more minority governments, some
coalitions, and more consensus style law-making. And more frequent
elections too, unless you curb the non-confidence vote. You would
not have to change the ridings, the number of MLA's, nor the
parliamentary one-seat one-vote convention. The simplicity of this
proposal is its greatest appeal -- the vast majority would likely
accept it. But I have some serious reservations I will address
later.
Things That Go Bump In The Day
First the notion of NOTA: None Of The Above. The idea that people
who vote NOTA should, on the strength of that preference, be
appointed by lot to rule is bizarre and totally without merit. Let
them get elected. Spoiling a ballot, or refusing to vote, is the
exact equivalent of a NOTA vote.
Legitimately, the advocates of NOTA are concerned with the behavior
of political parties in their membership, candidate selection, and
nomination practices. Unfortunately, the subject of political
parties and their functioning is at least as complex as electoral
systems. Albeit closely related, political parties, and the rules
that should govern them, are the proper subject matter for yet
another Citizens' Assembly.
Second the majoritarian systems: AV and Run-off. To reach for a
majority every time in order to have legitimacy is to reach too
far. Real life is simply not that cut and dried. We must find
legitimacy in less rigid and arbitrary standards. I think
legitimacy is achieved where there are no wasted votes, whatever
the outcome.
The fundamental error of majoritarian systems is that they treat
the incidental ranks of isolated preferences as if they were
intentional ranks of integrated preferences. Majoritarian systems
are simply wrong-headed. False assumption leads to forced majority
leads to false majority. The first-dropped back-marker (the Garden
Party) might have been "everyone's second choice".
In terms of outcome, they are biased in favour of the leading
contenders and against the back-markers. In terms of voting power,
they are biased in favour of those whose views are the least
representative of the constituency (the supporters of the
back-markers), and against the leading contenders, whose supporters
have no second vote. But most of all, majoritarian systems are
biased against middle contenders, who often neither win nor whose
supporters get a second vote. I'm sorry, Nick, AV is humbug. If
anyone gets a second vote, everyone should get a second vote. Let
the voters, not the voting system, decide. Majoritarian systems are
a bad choice.
Third, STV: AV on steroids. STV is the way you do AV in a
multi-member constituency. Because the constituency is
multi-member, you cannot use an absolute majority as the criterion
for a win. You have to use a quota (Droop) as the benchmark of a
win. The more seats you have to fill in the constituency, the lower
the quota [see Farrell, p.130]. The absolute majority of AV is
divided evenly accross the number of seats that have to be filled.
STV is just another majoritarian system. All the objections against
the other majoritarian systems apply to STV. In addition the
counting system is so complex as to require a computer algorithm to
complete. Consequently, the average citizen cannot monitor it for
honesty, neither in the count nor in the algorithm. Anyone with a
Grade Three education can accurately monitor a Borda count.
Furthermore we have had AV and multi-member ridings in BC before.
We got rid of them as unsatisfactory and undemocratic.
The single redeeming characteristic of STV is its capacity to
produce broad PR -- the more seats per constituency, the greater
the PR. But, if you think about it, this tendency is true for most
voting systems. FPTP would produce perfect PR if all the seats of
the Province were in one riding. So STV then has nothing special to
recommend it. It is a dog. And now Nick, ever the politician, does
not want to say "PR" out loud in public because it "won't sell
beyond Hope". I am sure Nick knows a lot better than I do what will
sell beyond Hope. But I think his plan involves an awful lot of
kerfuffle just to get a little PR. My "made in BC" plan achieves a
lot more PR for a lot less trouble [Kennedy 0740}. Indeed, my
flawed proposal in the present submission regarding the Most
Favourite and Best Compromise alternatives would probably achieve
as much PR as STV would. And it only involves changing a ballot.
Academe: The Nonsense of Condorcet and The Irrelevance of
Arrow
Basically Condorcet does the reverse of what the majoritarians do.
Condorcet takes the intentional ranks of a roster of integrated
preferences and treats them as if they are the incidental ranks of
isolated pairwise preferences. Like the majoritarians, Condorcet is
just wrong-headed. Pairwise comparisons are isolated; ranked
preferences are integrated. The psychology and the results are
importantly different. Condorcet's elegant math (combinatorics)
applied to voting makes no more sense than multiplying your hat
size by your shoe size.
Furthermore, valid science demands that if you want pairwise
results, you have to present pairwise alternatives. In three
alternatives there are 3 pairs (AB,BC,CA); in five, 10; in ten, 45;
in twenty, 190. Such ballots are out of the question. In practice,
of course, they would also include oodles of ties. Even where his
supporters allow him to manipulate his data, there are ties and no
Condorcet winner 10% of the time. There is a small handbook of
different methods which attempt to resolve these ties. Even if the
Condorcet method were correct, a 10% failure rate could never be
trusted in real politics.
Moreover, Condorcet is profoundly biased in favour of the median
candidate, who can be the Condorcet winner even when his FPTP count
puts him third or worse. This is a source of pride to the
supporters of Condorcet. The people of BC would be outraged. Hands
down, Condorcet is probably the best and most powerful method of
electing the candidate "nobody wants". Consequently, the Condorcet
criterion is humbug.
Arrow adopted the Condorcet criterion (whoever wins the most
pairwise comparisons should be the winner) and added his own:
Independence to Irrelevant Alternatives. On the ground, that means
"some candidates are irrelevant".
There is no place in democracy for a fundamental concept of an
"irrelevant candidate". All candidates are relevant until the
individual voter decides some are not. No pundit or economist can
speak for the electorate and legitimately identify any candidate as
"irrelevant". Only the voter has the right to that executive
decision.
Arrow won a Nobel Prize for his conclusion that logically only a
dictator can choose between three alternatives. So, these two guys
and Arrow want to go on a fishing trip, but they each prefer a
different lake. Guess who wants to be dictator. Balderdash baffles
brains. Do not let it claim you as its next victim. In the end,
political science is usually done better by political scientists
than by mathematicians and economists.
Approval Voting: The Choice of Mandarins
Approval voting has been adopted by, among others, academics,
clergy, mathematical associations, and the UN. People in these
professions are likely to be definitive about what is wrong, come
up with more questions than answers, and work in milieus
characterized by indecision. They want to avoid divisiveness
(strongly held opposite opinions and platforms), factionalism
(political parties and movements), and strategizing (election
strategies and voters strategies). Basically, they do not like the
hurly-burly of democracy. They believe that important matters
should not be decided by voting. Rather, such decisions should be
based on superior science, superior philosophy, superior values,
and superior intelligence. Approval voting feels comfortable to
them.
Approval voting uses a roster of alternatives, but does not rank
them. Approval voting "rejects preference" in favour of
"tolerance". Ironically though, without rejection no decision can
be made with Approval voting. Voters' preferences are limited to
two: approve, or disapprove, which we can think of as "one's" and
"zero's". In the end, Approval voting is biased in favour of
indecision and convergent thinking and alternatives. It is biased
against decision (except rejection, disapproval, exclusion), and
against divergent thinking and alternatives. "Conform" is its
message.
Approval works like this. Imagine a grid with four candidates
accross the top (A,B,C,D), and ten voters down the side
(1,2,...10). there are forty squares into which one's and zero's
can be put. The candidate with the most one's wins. Each square
holds either a one or a zero. Each voter has four votes, and they
can be any arrangement of one's and zero's wanted. Simple.
Suppose all ten voters approve of all four candidates -- a one in
every of the forty squares. The result? No winner. Approval voting
requires disapproval (rejection, exclusion). With four candidates,
a minimum of three rejections is necessary -- one zero each for
B,C,D -- for A to win. Where voter 10 provides those three zero's,
they override the 27 approvals for B,C,D supplied by the other 9
voters. A wins by one vote supplied by one voter, whose opinions
are contrary to those of the huge majority. This result is bizarre
and profoundly undemocratic.
Now suppose there a zero's in all the squares but one. Voter 10
approved A, and A wins. Again the result is bizarre and profoundly
undemocratic. Only when the electorate is evenly split (plus or
minus one) does the result approach a democratic one. This is the
reverse of normal democratic voting where a landslide satisfies
legitimacy more than a close finish. Leave it to the mandarins to
march lockstep and boldly into the future, derriere first.
The positive contribution of Approval to rational voting is,
ironically, exclusion.
And The Winner Is...
The first preference ballot, and its expansion, the ranked roster
ballot are the best choices. What remains is a discussion of their
counts, biases, and contexts.
Unbeknownst to most people, the first preference ballot can be
counted two ways. If just a single alternative is the result
required, then we count the ballots in the old familiar FPTP or
plurality fashion. On the other hand, if we want to know how much
support was received by each first preference, we can count the
ballot proportionally. Or we can do both counts as I propose in
Kennedy
0740. Under my proposal there, the plurality count determines
who wins the seat, and the proportional count (cumulated over all
ridings) determines the first preference support for all the
political parties in the Province. The seat winners get to vote an
even share of the province-wide support for their Party on the
floor of the Legislature.
The plurality count of the first preference ballot is biased in
favour of change because a relatively small shift in voter support
can change the seat winner. Theoretically, the more candidates
running in the riding, the less it takes to cause a change.
Where the plurality count is used in a sole riding (like the
Vancouver at-large mayor's election), the count is biased in favour
of many candidates.
The proportional count is cumulated province-wide and thus the
Province is treated as a single riding. Done this way, the
proportional count is biased in favour of a variety of parties.
The context we are talking about is the polity of the whole
Province. Large polities, unlike small ones (unions, etc.), resist
change. Thus the first preference ballot provides a needed impetus
to change and variety.
Where the plurality count winner results are simply added up over
all the ridings, distortion away from proportional representation
sets in. Also the voters want to make their votes count
province-wide, so they tend to favour one of the two front running
parties in their local candidate selection. This voter behavior
produces a bias in favour of two parties in the Province.
The proportional count I propose would eliminate disproportional
distortion and incline the voters to choose more broadly from a
variety of parties. The voters' votes would count province-wide,
and there would be a multi-party system.
The first preference ballot is the best because it answers two
questions: "What is the Most Favourite alternative?" and "How much
support did each Favourite receive?" The ranked roster ballot is
the second best ballot, and it also answers two questions: "What is
the Best Compromise alternative?" and "What is the prioritized list
of Compromise alternatives?" These are the two best ballots on the
planet. They answer those four questions accurately and
consistently.
Analytically, the first preference ballot and the ranked roster
ballot are intimately intertwined. The first rank of the ranked
roster ballot is mathematically identical to the first preference
ballot. While I have referred to the ranked roster as an expansion
of the first preference ballot, it would be equally valid to think
of the first preference ballot as a segment or calf of the ranked
roster ballot. The first preference count is an isolated count of
the first rank. The ranked roster count is a global count of all
the ranks. There are two isolated counts, and two global counts.
Each of the four counts answers the four questions.
The ranked roster of integrated preferences usually receives a
Borda count. So in the literature it is usually called a Borda
ballot.
Condorcet and the mathheads try to stuff preferences into the
sausage machine of logic. Borda had more sense. Borda's ballot was
attacked for "promoting" strategic voting rather than "sincere"
voting. Most mathematicians whip out notation to defend themselves.
Borda spoke of honesty.
Borda was a practical mathematician who studied the accuracy of
clocks in order to improve navigation (longitude). In his own
quiet, obscure way, he probably saved the lives of thousands of
sailors. The Borda count assigns points in the exact reverse order
of the available ranks (see Preferences, above).
Strategic voting is only effective when a large number of voters
employ exactly the same kind of strategic vote. That looks like a
groundswell of voter sentiment to me. As a democrat, I do not think
it is legitimate for anyone to say such voters are wrong in their
choice to vote strategically. Such a groundswell is as sincere as,
and maybe even more sincere than, any other kind of "sincere"
voting. The electorate is always "right", and always has the right
to be "unwise". The "wise" have an obligation to educate and
persuade the electorate.
Strategic voting can be viewed as a legitimate countermeasure to an
ineffective or corrupted political system. Since the possibility of
ineffectiveness and corruption always exists, the possibility of
strategic voting should also continue to exist.
The only kind of strategic voting that is truly distasteful is
where the voters are put in a corner so that they have to vote for
an alternative they do not like in order to rid themselves of, or
prevent themselves from getting, a government they cannot stand.
This happens all too often in our FPTP, SMP, one seat-one vote
system. My proposals remedy this by removing the corner.
A more sophisticated Borda ballot via Approval (exclusion) voting
permits the voter to leave any selection blank, put a zero after
it, or cross it out in rejection, and only rank the remaining
candidates. The voter is then free to apply any of the available
ranks to the remaining candidates.
For example, a voter can exclude two candidates on a roster of
five. He then has five ranks that he can apply to candidates A,B,C
whom he wants to rank. He has a total of ten different ways he can
rank A,B,C, as follows: 1-2-3, 1-2-4, 1-2-5, 1-3-4, 1-3-5, 1-4-5,
2-3-4 , 2-3-5, 2-4-5, 3-4-5. The different ranks have different
point values for the candidates. The gaps the voter leaves give a
more accurate expression of his opinions. Or the gaps can be
thought of as places for candidates he wishes were running. For the
mathheads, the gaps represent a kind of quasi-interval spacing to
rank ordinal data, and thus add a bit of precision to the results.
In democratic terms, the Borda ballot with exclusion maximizes
voter choice, and gives the voter "sovereignty over his ballot". It
also multiplies the different kinds of possible personal strategic
votes, and thereby tends to nullify the collective effect of
strategic voting.
Like all ranked roster ballots, Borda is biased towards the median
candidate, and by extension the status quo. If we used a Borda
ballot in our federal ridings, we would probably never be able to
get rid of the Liberals as the ruling party -- ask Joe Clark! If we
used a Borda ballot in BC ridings (as I proposed here at the end of
Preferences), we would get wonderful temporary relief from our
migraine of polarization. However, it would probably lead to the
same person getting elected time after time for decades. That
situation would lead to "ridings as fiefdoms" and "ward boss"
politics, which we definitely do not want. Thus in the long run we
probably would not be able to get rid of the dithering,
hand-wringing, politically correct, corrupt Middle Road Party. We
definitely do not want that either. So while I voiced the proposal
for perspective, I do not recommend it because of its long run
consequences. We need the impetus for change and variety that the
first preference ballot provides at the riding level.
Large polities resist change -- they want just enough to scratch
the current itches. The Borda ballot is most effective in contexts
where lots of change is desired. For example, a Borda global count
would work well for an amateur theater company deciding what plays
to put on next year. The result, based on integrated preferences,
would be a prioritized list of compromise choices. Such a list
would be a useful tool in the Provincial electoral system.
My Seven Cent Solution (Kennedy 0740) would result in near-perfect
PR; PR produces a multi-party system; and a multi-party system
leads to coalitions. The Independent Commission Report on PR in
Britain (ICPR)[CA website: other links, other countries, third
item] lists five drawbacks of coalitions (ICPR,p.103,sec.12.15):
1. The actual government is unknown after the election -- it is
dependent on post-election party bargaining.
2. Accountability is not assignable to a specific party in the
coalition.
3. Smaller parties can hold larger parties to ransom to get what
they want.
4. Coalitions are unstable and more likely to collapse. And they
are less dynamic and slower at policy making.
5. When coalitions are comfortable with each other and not
unstable, they are hard to remove.
The answer of course is to give the electorate some power over the
coalitions and the direction of policy. I propose a province-wide
party preference Borda ballot with exclusion and global count. This
would winnow out splinter parties and produce a prioritized list of
Compromise parties to form a coalition with. The most successful
party from the cumulated popular vote from the ridings would be
obliged to follow the priorities when forming a coalition. Thus the
electorate would have a good idea of what the actual government
would be, and therefore know who to hold accountable. By
controlling who the members of the coalition are, the electorate
would be able to (a) have some control over the general direction
of policy, (b) break up comfortable coalitions, (c) minimize the
effect of splinter parties, and (d) introduce some stability to
coalitions by making the other options remote. This proposal, I
think, answers the ICPR's concerns about the drawbacks of
coalitions.
Having had so much to say, it is only fair that I respond. I feel
obliged and would be pleased to any questions or criticisms from
the Members of The Citizens' Assembly. My email is on my
submissions. So is my phone. Feel free.