3.—The Droop-Gregory Method.—This method, advocated by Professor Nanson, of the Melbourne University, is claimed to entirely eliminate the element of chance. The Gregory plan of transferring surplus votes is defined as a fractional method. If a candidate needs only nine-tenths of his votes to make up his quota, instead of distributing the surplus of one-tenth of the papers all the papers are distributed with one-tenth of their value. Reverting to our former example, if a candidate is marked second on 550 out of 1,100 votes, the quota being 1,000 and the surplus 100, then instead of selecting 50 out of the 550 papers, the whole of them would be transferred in a packet, the value of the packet being 50 votes, or, as Professor Nanson prefers to put it, the value of each paper in the packet being one-eleventh of a vote. Should this packet contribute to a new surplus the third choices on the whole of the papers are available as a basis for the redistribution. The packet would be divided into smaller packets, and each assigned its reduced value. It might here be pointed out that the use of fractions is quite unnecessary, the value of each packet in votes being all that is required, and that the-same process may be used with the Hare-Clark method to avoid the chance selection of papers. The only real difference is this: that when a surplus is created by transferred votes Mr. Clark distributes it by reference to the next preference on all the transferred papers, and Professor Nanson by reference to the last packet of transferred papers only—the packet which raises the candidate above the quota.

Which of these methods is correct? Should we select the surplus from all votes, original and transferred, as Sir John Lubbock proposes; from all transferred votes only, with Mr. Clark; or from the last packet only of transferred votes, with Professor Nanson? Consider a group of electors having somewhat more than a quota of votes at its disposal. If it nominates one candidate only every one of the electors will have a voice in the distribution of the surplus, but if it puts up three candidates, two of whom are excluded and the third elected, Mr. Clark would allow those who supported the two excluded candidates to decide the distribution of the surplus, and Professor Nanson only those who supported the last candidate excluded. Both are clearly wrong, for the only rational view to take is that when a candidate is excluded it is the same as if he had never been nominated and the transferred votes had formed part of the original votes of those to whom they are transferred. Whenever a surplus is created it should therefore be distributed by reference to all votes, original and transferred. As regards these surpluses, Mr. Clark and Professor Nanson have adopted an arbitrary basis, which is no more than Sir John Lubbock has done; and they have therefore eliminated the element of chance only for surpluses on the first count. It may be asked, Why cannot all surpluses be distributed by reference to all the papers, if that is the correct method? The answer is that the complication involved is enormous. Yet this was the plan first advocated by Professor Nanson, who wrote, in reply to a definite inquiry how the Gregory principle was applied:—"I explain by an example. A has 2,000 votes, the quota being 1,000. A then requires only half the value of each vote cast for him. Each paper cast for him is then stamped as having lost one-half of its value, and the whole of A's papers are then transferred with diminished value to the second name (unelected, of course). The same principle applies all through. Whenever anyone has a surplus all the papers are passed to the next man with diminished value." Now, the effect of this extraordinary proposal would be that the whole of the papers would have to be kept in circulation till the last candidate was elected, with diminishing compound fractional values. In a ten-seat electorate a large proportion would pass through several transfers, and would towards the end of the count have such a ridiculously small fractional value that it would take several millions of the ballot-papers to make a single vote! It is no wonder that this method was abandoned when the complications to which it would lead were realized.

A simple method of avoiding this complexity would be to treat transferred surplus papers as if the preferences were exhausted. It must be remembered that in all transfers a certain number of papers are lost owing to the preferences being exhausted, and the additional loss would be small. Thus at the first Hobart election 206 votes were wasted, and this number would have been increased by two only. Every surplus would then be transferred by reference to the next choice, wherever expressed, on both original papers and papers transferred from excluded candidates.

It might be provided, however, for greater accuracy that all papers contributing to surpluses on the first count only should be transferred in packets. Should these contribute to a new surplus, it should be divided into two parts, proportional to (1) original votes and votes transferred from excluded candidates, and (2) the value of the packet in votes. Each part would then be distributed proportionally to the next available preferences wherever expressed. To divide the packets into sub-packets is a useless complication. The loss involved in neglecting them would usually be less than one-thousandth part of the loss due to exhausted papers.

Having now dealt with the main features of the different variations of the Hare system, we may proceed to consider some details which are common to all of them. A difference of opinion exists, however, as regards the quota. Sir John Lubbock and Professor Nanson advocate the Droop quota, which we have shown to be a mathematical error; Miss Spence and Mr. Clark use the correct quota.

The Wrong Candidates are Liable to be Elected.—The Hare system may be criticised from two points of view; first, as applied to the conditions prevailing when it is introduced, and, secondly, as regards the new conditions it would bring about. Its advocates confine themselves to the first point of view, and invariably use illustrations based on the existence of parties.

We readily grant that if the electors vote on party lines, and transfer their votes within the party as assumed, the Hare system would give proportional representation to the parties; but even then it would sacrifice the interests of individual candidates, for it affords no guarantee that the right candidates will be elected. The constant tendency is that favourites of factions within the party will be preferred to general favourites. This at the same time destroys party cohesion, and tends to split up parties. Nor can this result be wondered at, since the very foundation of the system is the separate representation of a number of sections.

One reason why the wrong candidates are liable to be elected is that the electors will not record their honest preferences if the one vote only is effective. They will give their vote to the candidate who is thought to need it most, and the best men will go to the wall because they are thought to be safe. Mr. R.M. Johnston, Government Statistician of Tasmania, confirms this view when he declares—"The aggregate of all counts, whether effective or not, would seem to be the truer index of the general favour in which each candidate stands, because the numbers polled at the first count may be greatly disturbed by the action of those who are interested in the success of two or more favourites who may be pretty well assured of success, but whose order of preference might by some be altered if sudden rumour suggested fears for any one of the favoured group. This accidental action would tend to conceal the true exact measure of favour in the first count." If this statement means anything it is that the three preferences which are required to be expressed should have been all counted as effective votes at the Hobart election instead of one only; and this is exactly what we advocate. It is also admitted that when two candidates ran together at the first Launceston election the more popular candidate was defeated; and again the Argus correspondent writes of the recent Hobart election:—"The defeat of Mr. Nicholls was doubtless due to the fact of his supporters' over-confidence—nothing else explains it. Many people gave him No. 2 votes who would have given him No. 1 votes had they not felt assured of his success."

A second reason why the wrong candidates are liable to be elected is that the process of elimination adopted by all the Hare methods has no mathematical justification. The candidate who is first excluded has one preference only taken account of, while others have many preferences given effect to. We have shown that this glaring injustice was recognized by Mr. Hare, and only adopted as a last resort. Professor Nanson admits that "the process of elimination which has been adopted by all the exponents of Hare's system is not satisfactory," and adds—"I do not know a scientific solution of the difficulty." To bring home the inequity of the process, consider a party which nominates six candidates, A, B, C, D, E, and F, and whose numbers entitle it to three seats, and suppose the electors to vote in the proportions and order shown below on the first count.

FIRST
COUNT.		SECOND
COUNT.		THIRD
COUNT.		FOURTH
COUNT.
7-voteADEFBCADEBCAEBCABC
6-voteEFDACBEDACBEACBACB
5-voteCEBDFACEBDACEBACBA
4-voteBDFACEBDACEBACEBAC
4-voteDCEFBADCEBACEBACBA
3-voteFBAECDBAECDBAECBAC