The (almost really) Complete Works of Lewis Carroll

[In the following suggestions, the word “College” is to be taken to mean “College, or College and Hall combined, or the Body of Non-Collegiate Students.”]

In any system, by which turns in electing Proctors are to be assigned to Colleges with a frequency which shall be proportional to the size of each College, the first question to be settled is, what criterion of size should be adopted.

Several such criteria have been suggested, e. g. the number, on the College books,

The last-named seems to be at once the most simple, the most equitable as regards aspirants to the office, and the most likely to be accepted by the University. This is the criterion adopted in the following suggestions.

In what follows, the phrase “eligible members” is to be taken to mean “members eligible as Proctor.”

If any other criterion of size be prefered to the one here adopted, this phrase may be replaced by “members of Convocation,” or by any similar phrase, without rendering any other change necessary.

Assuming, then, that the claim of any College, to elect in any given year, should be taken as proportional to its number of eligible members, at least in the case of two Colleges who have been waiting equally long for a turn, it may also be assumed that, in the case of two Colleges of equal size who have been waiting unequally long, the claim should be taken as proportional to the number of years of waiting. If these two conditions be granted, it follows by ordinary “Double Rule of Three” that, when both elements vary, the claim is fairly represented by the product of the two numbers.

The second question to be settled is whether the data, used in determining for any given year the claims of the several Colleges to elect in that year, should be merely the most recent obtainable, or should be an average, taken over previous years. It can hardly be necessary to point out that, if the number of members in a College has changed suddenly within the year, to multiply the new value by the number of years of waiting, and thus to make the recent change have the same effect as if it had occurred many years previously, is to give to the fluctuation far more than its due effect. The obvious answer to this question is, that the number, representing the claim of each College, should be the product of the number of years of waiting and the average annual number of eligible members for those years.

Now the average number of members, for a series of years, multiplied by the number of years, is identical with the sum-total of the annual numbers. Thus the “claim” for any given year may be found by simply adding together these numbers, for all the years elapsed since the last election; and, when it is once known for any given year, the addition of the number of members for that year will give the “claim” for the next year.

It is obvious that the two Colleges, whose “claims” in any given year stand highest, are the two who should elect the Proctor for that year.

The third question to be settled is, how long beforehand it is desirable to know what Colleges will be entitled to elect in any given year.

It would seem that three or four years, at the outside, would be amply sufficient notice. It is conceivable that one, who was tolerably certain of being elected by his College in its next turn, might make his plans dependent on the question whether that turn would occur in three years or in four: but it is extremely unlikely that he would care to know whether it would occur in seven years or in eight. In the system here suggested, the rotation of Colleges would always be known rather over four years in advance.

The fourth question to be settled is, at what intervals the system of rotation should be re-adjusted, so as to give due effect to the fluctuation, in each College, of the number of its eligible members.

A Cycle of 30 years is undoubtedly too long for this purpose, and it is fairly open to the charge, brought against it by Dr. Moore, that, “granting that it was approximately fair when first made out, it would almost certainly be far from corresponding with existing facts long before the Cycle of 30 years had run its course.”

A Cycle of 5 years, re-adjusted once in five years, is less open to this charge, but labours under one of two serious disadvantages, which may be best stated as a dilemma. If it were computed on the most recent data, it could only be published just before coming into use; so that, towards the end of each period, there would be no certain information to be had as to future elections. If, on the other hand, it were published four or five years before coming into use, it would, though quite sufficiently in accordance with the facts in its first year, become less and less so from year to year; and there would always be a sudden change, with the introduction of each new Cycle, from the use of data ten years old to that of data only five years old.

But, granting that it is necessary to base the computation of claims, for any one year, on the data of five years back, in order that the names of the Colleges electing in any year may be published five years beforehand, there seems to be no reason for doing more than this. That is to say, if the names for the 10th year be published in the 5th, those for the 11th in the 6th, and so on, the order of rotation will always be known for the next 5 years, while the data, used in computing the claims for any one year, will always be neither more nor less than 5 years old.

The principle here adopted is that, in the year 1900 for example, the claims for the year 1905 shall be computed and published; and that the claim of each College shall be the product of two numbers—one, the number of years elapsed, in 1905, since its last turn, the other, what is assumed as its average annual number of members for those years, though it will really be a similar average taken, from the year 1900, back to its last previous turn.

It would be desirable for Council to publish in each Michaelmas Term, along with the list of members of Convocation the names of the ten Colleges entitled to elect during the next five years. Also, as it would be well to fix on a definite day, for which each College should take the annual census of its eligible members, Michaelmas Day might be found convenient for this purpose.

In order to commence the new system in Michaelmas Term, 1886, it would be necessary to compute and publish the claims for 1889, 1890, and 1891. Those for 1889 would have to be computed by multiplied together, for each College, the number of years elapsed, in 1889, since its last turn, and the best attainable average of its annual number of eligible members. It would probably be most satisfactory, instead of going back into past years, to accept the returns for Michaelmas Day, 1886, as the average required.

This method would be easily worked out of all but 3 of the 22 Bodies contemplated in the new Statute.

But in the case of Keble and Hertford Colleges and the body of Non-Collegiates, a different method would be needed, since there is no previous “turn” to date from. For each of these Bodies an ideal “period of waiting” must be assigned: and this would equitably be half of the interval of years at which the “turns” of that Body ought to recur. To calculate this interval, it would be necessary to add together the average numbers of eligible members of all the Colleges, and to divide their total by the number of the College in question; and then to halve this quotient, since two Colleges elect in each year. This may sound complex; but, since the number of eligible members is used first as a divisor and then as a multiplier, it may be ignored altogether, and the practical result is to assign to each of these three Bodies, as its claim for 1889, one-fourth of the total number of eligible members in the University.

In the (probably rare) event of the two “claims” occurring, the rule might be adopted of giving precedence to the College that had waited longest: but this rule should be reversed, if it happened again with the same two Colleges.

The Table published (say in the year 1900) might be of the following form:—

The numbers in the 2nd column would, except for the 2 Colleges electing that year, be added to those in the 3rd, to give those in the 4th. For these 2 Colleges, the number in the 3rd would be repeated in the 4th.

The publication of such a Table would enable any one to calculate for himself, approximately, the order of rotation for any number of future years.

Suggested Form of Statute

Whereas it is expedient to revise the Procuratorial Cycle and to determine the qualification of the members of the several electing Bodies, the University enacts as follows.

In Statt. Tit. XVII. Sect. iv, § 1 (p. 218, ed. 1884) shall be struck out, and the following new subsection shall be substituted:—

1. Of the Election of Proctors

There shall be two Proctors, who shall be elected annually on the Wednesday after the first Sunday in Lent. In and after the year 1889, they shall be elected by the following Bodies, in an order to be determined as hereinafter provided.

For the purposes of this section members of St. Edmund Hall shall vote with Queen’s College, and New Inn Hall shall be deemed to have been united with Balliol College, and St. Mary Hall with Oriel College.

Each of the above-named Bodies shall, immediately after Michaelmas Day, in and after the year 1886, furnish to Council a list of such members of Convocation as were on that day members of the said Body and eligible as Proctor. And Council shall publish, in Michaelmas Term, in and after the year 1886, the names of the ten Bodies entitled to elect Proctors for the five years next ensuing.

The names for the year 1889 shall be determined by multiplying, for each Body, the number of its eligible members by the number of years elapsed, in 1889, since its last turn. The products shall be taken as the claims for that year, and the two Bodies, whose claims atand highest, shall elect the Proctors for that year. And the claims for each subsequent year shall be computed by taking, for each Body, the last-returned number of its eligible members, and adding thereto its claim for the preceding year: but such addition shall not be made for the two Bodies electing in the said previous year.

To each of the three Bodies not included in the present Cycle, namely, Keble and Hertford College and the Body of Non-Collegiate Students, shall be assigned, as its claim for the year 1889, one-fourth of the total number of eligible members in the University.

If the name of any member of Convocation appear in more than one list at the same time, it shall be counted only in the list of that Body in which such member pays, or has compounded for, his University Dues.

The effect of the proposed Statute will be that the number, taken as the claim of each Body to elect in any given year, will be proportional to the number of years elapsed, in that year, since its last turn, and also to the average annual number of its eligible members. Hence the number of turns, assigned during any given period to each Body, will also be proportional to the average annual number of its eligible members.

The effect of assigning to each of the three Bodies, Keble and Hertford Colleges and the Body of Non-Collegiate Students, as its claim for 1889, one-fourth of the total number of eligible members in the University, is exactly the same as if each had had a previous turn, and the number of years elapsed had been, in each case, one-half of the interval at which the turns of that Body ought to recur.