PREFERENTIAL VOTING, THE BLOCK VOTE, ETC.
+Preferential Voting.+--Laplace, the great mathematician, to whom we owe
so much of the theory of probability, showed more than a century ago
that although individual electors may have very different views as to
the relative merits of a number of candidates for any office, still the
expression of the degree of favour in which the candidates are held by
the whole body of electors will be the same if each elector be assumed
to have a uniform gradation of preference. Suppose that there are ten
candidates, and it is required to place them in order of general favour.
Each elector should be required to place the whole ten in the order of
his preference, 1, 2, 3, &c. Let the maximum degree of merit be denoted
by ten marks, so that every first preference will count as ten marks.
Then, although an individual elector might be disposed to give his
second preference only five marks, and the rest of his preferences, say,
two marks, Laplace demonstrated that it is most probable that the total
result would be the same if each elector be assumed to give his second
preference nine marks, his third preference eight marks, and so on.
Therefore, if all first preferences be multiplied by ten, second
preferences by nine, and so on in regular order down to last preferences
multiplied by one, the total number of marks will be an index of the
order in general favour. If there is one office to be filled, the
candidate with the highest number of marks should be elected; if there
are two offices, the two highest candidates, and so on.
But the assumed condition must be rigidly complied with; each elector
must express his honest preferences. Whether he will do so or not
depends upon the circumstances. Laplace recognized this element of human
nature, and declared that if electors are swayed by other considerations
independent of the merit of the candidates the system would not apply.
For instance, if the candidates are the nominees of a number of
independent sections, each of which is anxious only to secure the return
of its own candidate, and to defeat those who stand most in his way, the
tendency will be general to place the more popular candidates, those
whose success is most feared, at the bottom of the list, so as to give
them as few marks as possible. The result would be to favour mediocre
men, or even in extreme cases the most inferior.
Practically, therefore, the system is not applicable where any of the
electors are personally interested in the result. If a number of judges
were called on to decide the relative merits of several essays or prize
designs, and the competitors' names were not known to them, the system
might be used. But even in such a case a simpler method is available;
for, although it may be difficult to pick out the best, it is generally
easy to agree upon the worst. It is usual, then, to gradually eliminate
the worst, and when the number is reduced to two to take the decision of
the majority.
This process of elimination may be, however, combined with the
preferential system, and the result is more accurate than if one count
only be made. At the first count the candidate with the fewest marks
would be eliminated and his name struck out on all the papers. All those
under him on each paper would then go up one point in order of favour,
and further counts would be held, eliminating the lowest candidate each
time till the candidates were reduced to the number desired. This method
is very complicated, and involves a great amount of trouble.
Consider now the case of a voluntary association of individuals, such as
a club or society; and suppose that it is required to elect a president
or committee. The condition is clearly that he or they should be most in
general favour with all the members; and the question whether
Preferential Voting is applicable will depend on how united the members
are. Now, clubs are not usually, nor should they be, divided into
cliques or parties; indeed, if a serious split does take place it
generally results in the resignation of part of the club and the
formation of a separate organization. But in a live club it is
impossible to prevent slight differences of opinion; and an
officer-bearer who has the interests of the club at heart must often
offend small sections who want to exert undue influence. In an election
for president this office-bearer would stand no chance of election if
there are several candidates and any small section likes to put him at
the bottom of the list, so as to give him as many bad marks as possible.
This is the weak point in Preferential Voting; any small section can
ensure the rejection of a general favourite. The greater the number of
candidates the smaller the minority which is able to do this; dummy
candidates may therefore be introduced to make it more certain. The risk
would, however, be very much lessened if the process of gradual
elimination we have described were adopted.
When we come to the election of representatives to a legislature it is
evident at once that Preferential Voting is not applicable at all. We
have shown that the true condition required is not the return of
candidates most in general favour with both parties, but the return of
the candidates most in general favour with each party separately.
Preferential Voting would therefore only be applicable if the electors
of each party voted separately for its own candidates; and even then it
would be open to the objection we have already urged. If it were applied
to the two parties voting together the electors would certainly not be
influenced only by the merit of the candidates. They might record their
honest preferences as regards the candidates of their own party, but
they would naturally place the candidates of the opposing party in
inverse order of merit. The candidates most in general favour would be
those who represented neither party. Suppose there are three candidates
for a single seat, two representing large parties of 49 per cent, each,
and the third a small party of 2 per cent. The electors of the large
parties would be more afraid of one another than of the small party, and
would give their second preferences to its candidate. This candidate,
representing one-fiftieth of the electors, would then actually be
elected; he would receive 202 marks, and neither of the others could
possibly secure more than 200. Moreover, he would still be elected if
the process of elimination were adopted, since on the second count he
would beat either of the other candidates separately by 51 votes to 49.
These plain facts are indisputable. What is to be thought, then, of the
claim made by Professor Nanson that Preferential Voting, with the
process of elimination, is the most perfect system known for
single-membered electorates.
+The Block Vote.+--The Block Vote, General Ticket, or _scrutin de
liste_, is in general use when there is more than one seat to be filled.
Each elector has as many votes as there are members to be elected, and
the highest on the list, to the number of representatives required, are
successful. Dealing first with elections to a legislative body, the
system is eminently unjust to parties. A rigid control of nominations is
necessary in the first place, because any party which splits up its
votes spoils its chance. Each party will therefore nominate only as many
candidates as there are seats, and the stronger of two parties, or the
strongest of a number of parties, will elect the entire list. A minority
might in the latter case secure all the representation, but the
practical effect of the Block Vote is to force the electors to group
themselves into two parties only. It therefore has the same beneficial
effect as the single electorate of confining representation to the two
main parties. This is apparently nob recognized by Professor Nanson, who
writes, in his pamphlet on the Hare system:--"Contrast with this the
results of the Block system. With strict party voting, which has been
assumed throughout, each of the five parties would put forward seven
candidates. The seven seats would all be secured by Form, with 44 votes
out of a total of 125, and the remaining 81, or more than two-thirds of
the voters, would be wholly unrepresented." Does the Professor really
think that the 81 (who, by the way, are _less_ than two-thirds) would be
so foolish as not to combine and secure all the seats?
The exclusion of the minority in a single-membered electorate excites
only a feeling of hopelessness, but when it fails to secure a single
representative in an electorate returning several members, a spirit of
rankling injustice is aroused. The Block Vote has, therefore, never been
tolerated for long in large electorates. In the early history of the
United States many of the States adopted it, and sent to Congress a
solid delegation of one party or the other. This proved so unjust, and
operated so adversely to the federal spirit in promoting combinations of
States, that Congress, in 1842, made the single-membered electorate
obligatory on all the States.
In France it was adopted at the election for the Chamber of Deputies in
1885. The result as regards parties was about as good as with the single
electorate system. The Republicans and Conservative-Monarchists, whose
numbers entitled them to 311 and 257 seats respectively, actually
secured 366 and 202. But it was abandoned after a trial at this one
election.
The Block Vote was adopted in Australia for the election of ten
delegates from each colony to the Federal Convention. This was a work in
which all parties might fairly have joined together; and in most
colonies the people did select the best men, regardless of party. In
Victoria, however, the newspapers took on the _rôle_ of the "machine,"
and the ten candidates nominated by the _Age_ were elected. Many of the
supporters of the defeated candidates voted for some on the successful
list who just defeated their own favourites. Had this been foreseen they
would have thrown away these votes by giving them to those sure to be
elected or to those least likely to be elected. The injustice of forcing
each elector to vote for the whole ten is thus brought home. We are now
threatened with the adoption of the Block Vote for the Federal Senate,
and in some of the States for the House of Representatives as well; and
it is in the hope of preventing this wrong that the present book is
written.
So far we have been considering the Block Vote as applied to the
election of a legislature with two or more parties; we now propose to
consider it as applied to one party only. It is a matter of common
knowledge that the Block Vote, when used for such an election as that of
the committee of a club, works very well, and results in the return of
the candidates most in general favour with all sections. The reason is,
of course, that all sections work together, and members vote for the
best men, regardless of sectional lines. We will go further and say that
the Block Vote is by far the best method for such purposes, and is
superior even to Preferential Voting. In the first place it is free from
the defect that a small section can ensure the rejection of a general
favourite; and in the second place it rests on at least as secure a
theoretical basis. To fix our ideas, suppose there are ten candidates
for five members of a committee. Laplace assumed (1) that each member
would have a knowledge of the merits of all the ten candidates, (2) that
his estimate of the respective candidates would vary arbitrarily
between nothing and a maximum degree of merit, (3) that each member
would express his honest preferences. The Block Vote, on the other hand,
assumes (1) that each member can pick out the five best candidates, and
therefore express his opinion as to how the committee should be
constituted, (2) that he will be inclined to place these five candidates
on one plane of favour and the other five on one plane of non-favour. We
submit that the latter assumptions agree more closely with the actual
state of affairs. The members can distinguish between candidates who
have merit and those who have no merit or of whose merit they are
ignorant; to force them, therefore, to place all the candidates in order
of preference is to make them express preferences where none exist.[8]
On the whole, then, the Block Vote is more likely to place the
candidates in their real order of favour.
But some reservation must be made. The Block Vote works best when the
number of candidates does not exceed two or three times the number of
vacancies. Suppose, first, that the candidates present in the final
result a fairly regular order of favour from lowest to highest. Each of
the successful candidates will then be supported by at least an absolute
majority of the members, providing the number of candidates be not
greater than twice the number of vacancies. But if there are four or
five times as many candidates as vacancies, none of the successful
candidates will have the support of a majority of the members. On the
other hand, however, the candidates do not usually present a regular
order of favour from lowest to highest when there are a large number of
candidates, for there may be a long "tail" of candidates who receive
very few votes. The following general rule may therefore be laid
down:--The Block Vote works best when the total votes given to rejected
candidates do not exceed the total votes given to successful candidates.
The difficulties indicated above were met by the Australian Natives'
Association by a plan which provided that no candidate should be elected
except by an absolute majority of the voters. The Block Vote is used
throughout; and if at the first ballot the required number of candidates
do not obtain an absolute majority a second ballot is held, from which
those at the bottom of the poll and those who have been elected are
eliminated. This process is continued till all the vacancies are filled.
Four or five ballots are sometimes required, and the proceedings become
very irksome. A sub-committee was recently appointed to investigate the
subject, and reported in favour of the Preferential System with one
count only. The process of elimination was considered too complicated to
be practicable. Now, the conditions presented by these elections, in
which a very large number of candidates are generally nominated, are
precisely those in which Preferential Voting lends itself most easily to
abuse. An insignificant minority may defeat a candidate who should be
elected, by placing him at the bottom of their lists.
A variation of the Block Vote may be suggested which is much simpler and
better. The preferential ballot papers should be used, and two counts
should be made. At the first count the primary half of the preferences
should be counted as effective votes, and the candidates should be
reduced to twice the number of vacancies. A second count should then be
made of the ballot papers, using the Block Vote. All or nearly all the
candidates would then obtain an absolute majority, and it is practically
impossible that any candidate should be eliminated by the first count
who would have had any chance of election in the second.
This plan is far superior to the original method. It is right that
members who vote for candidates who are hopelessly out of it should be
allowed to transfer their votes; but it is not right that members who
first help to elect some candidates at one ballot should have the same
voting power as others at subsequent ballots.
The Hare system is sometimes advocated for clubs on account of its
supposed just principle. Any live club which adopts it runs the risk of
disruption. It merely encourages the formation of cliques and sections;
any slight split would be accentuated and rendered permanent.
+The Limited Vote.+--The injustice of the Block Vote led to the
introduction of the Limited Vote, which allows the minority some share
of the representation. We have seen that the Block Vote forces each
party to try to return all the representation, and of course one party
only can succeed. But if neither party be forced to try to return more
than it is entitled to each party will get its correct share of
representation, providing both parties are equally organized. This leads
to the Limited Vote, in which each elector has a number of votes
somewhat less than the number of seats.
The Limited Vote was used in England for a number of three-seat
electorates, which were created by the Reform Bill of 1867, each elector
being allowed to vote for two candidates only. By this means the
majority would usually return two candidates and the minority one. Thus
the Limited Vote has the same advantage as the Block Vote and the single
electorate system, that it tends to confine representation to the two
main parties, but it creates an artificial proportion of representation
between them. Moreover, it renders strict party organization even more
necessary, since each party must arrange to use its voting resources to
the best advantage. Consider the three-seat electorate, for instance.
The minority will, if it is wise, nominate two candidates only; and the
majority may nominate either two or three. But if the majority does
divide its votes among three candidates it runs the risk of securing one
only. It can do so safely when two conditions are fulfilled: first, it
must be sure of polling more than three-fifths of the votes; and,
second, it must arrange to distribute all its votes equally among the
three candidates. It is not surprising, therefore, to find that the
Limited Vote was responsible for introducing "machine" tactics into
England. In Birmingham, when Mr. Joseph Chamberlain organized the
Liberals and succeeded in carrying all three seats, the electors in each
ward were directed how to vote so that as few votes as possible might be
wasted. These three-cornered constituencies were abolished by the
_Redistribution Act_ of 1884; and Sir John Lubbock, reviewing the
experiment, declared--"On the whole, it cannot be denied that under the
Limited Vote the views of the electors have been fairly represented."
The system has also been tried to a smaller extent in the United States.
In New York 32 of the delegates to a constitutional convention were
elected from the State polled as one electorate, each elector being
allowed to vote for 16 candidates. Both parties were afraid to split
their votes, and the result was that each returned 16. The rest of the
delegates were elected in single-membered electorates, and of these the
Republicans secured 81 and the Democrats 47. It might here be pointed
out that the Republicans might have secured more than 16 of the
delegates from the State at large if they had nominated 20 candidates
and allowed the laws of chance to regulate their organization. Each
elector might have been directed to put the twenty names into his hat,
and to reject the first four he pulled out. The same evil is apparent in
Boston, where twelve aldermen are elected at large, each elector being
allowed seven votes. Each party nominates seven candidates only; and the
majority invariably elects seven and the minority five.
The Limited Vote is therefore not a satisfactory solution of the problem
of representation. It gives an artificial instead of proportional
representation, and it necessitates strict party organization and
control of nominations. At the same time it will generally give a very
fair representation if parties are not strictly organized, and might
well have been adopted for the Federal Convention, five or six votes
being allowed instead of ten. Newspaper domination would thus have been
prevented.
+Election of the Candidate Most in General Favour.+--It is often
required to ascertain the candidate most in general favour where one
party only is concerned, such as an election for leader of the
Opposition or president of a club; and the methods in general use are
very defective. We do not refer to the theoretical difficulty, which
perplexes some persons, of giving effect to the actual degree of favour
in which the candidates stand in the electors' minds, but to the simple
problem of finding out who is preferred most by the bulk of the
electors. Thus it is universally recognised that when two candidates
stand the candidate who has the support of an absolute majority of the
electors is entitled to election. Yet it is possible that the rejected
candidate may be nearly twice as popular. This might happen if the
majority held that there was little to choose between the two
candidates, while the minority thought they could not be compared. But
it is quite evident that such distinctions cannot be recognized; the
candidate who is preferred by an absolute majority must be elected. It
is when there are more than two candidates that the difficulty arises.
To elect the candidate who has most first preferences is open to very
serious objection; he may have a small minority of the total votes, and
each of the other candidates might be able to beat him single-handed.
The best way to overcome the difficulty is undoubtedly by some process
of gradually eliminating the least popular candidates till the number is
reduced to two; the candidate with the absolute majority is then
elected. We propose to consider the different ways in which elimination
might be made. We assume, in the first place, that each elector has cast
an advance vote--_i.e._, that he has placed all the candidates in order
of preference. The most primitive method is to eliminate at each
successive count the candidate who has least first preferences. This is
the method adopted in the Hare system, and we have already shown that
it is very defective; in fact, it is no improvement at all. The
eliminated candidate might be most in general favour, and might be able
to beat each of the other candidates single-handed. A second method is
to use Preferential Voting to decide which candidate should be
eliminated at each successive count. This is far superior, but it is
extremely complicated, and is open to the objection that when there are
a large number of candidates a small section may cause the rejection of
the general favourite. We propose to describe a method based on the
Block Vote which is much simpler, and which does not lend itself to
abuse. We have shown that the Block Vote works best when the candidates
can be divided into two equal sections of favour and non-favour. Suppose
there are four candidates, the first two preferences should therefore be
counted as effective votes, instead of the first preference only. The
eliminated candidate will then be the least in general favour. A second
count is then made of the three candidates left, and the first
preferences and half of the second preferences are counted as effective,
and the lowest again eliminated. The candidate who has an absolute
majority is then elected. The method may be indefinitely extended; if
there are five candidates the first two preferences and one-half of the
third preferences are counted, and so on. But when there are a great
many candidates more than one might be eliminated. Any number up to
eight could be safely reduced to four at the first count.
FOOTNOTE:
[8] The bracket principle introduced by Professor Nanson into the Hare
system involves a partial recognition of this fact.