The provisions for bye-elections are contained in sections 17 to 20.

(1) The elector is supplied three days before the election with copies of the various party lists; he is given as many votes as there are members to be elected; he may strike out any names and insert others in any of the lists supplied to him, or compose his own list; he may repeat the name of the same candidate three times, but no more; but in no case may the total number of names exceed the number of members to be elected.

(2) The Hagenbach-Bischoff rule, like the d'Hondt rule, aims at finding an electoral quotient which will allow all the seats to be allotted to the different parties without remainder. In the former rule this is found by trial. The following example explains its mechanism:--

Suppose, in an election for sixteen seats, five lists have obtained votes as follows:--

List. Votes.

A 5,537 B 9,507 C 3,885 D 4,769 E 377 ------- Total 24,075

The first quota is ascertained as prescribed in section 11. The number of votes is divided by one more than the number of vacancies, and the result is increased by one, thus:--

24075/(16+1) + 1 = 1417

It will be observed that this quota is identical with the Droop quota of the single transferable vote system. The totals obtained by each list are divided by this quota, as many representatives being allotted to each list as the list contains the quota. Remainders are ignored.

Lists. Votes. Quota. Representatives.

A 5,537 1,417 3 B 9,507 1,417 6 C 3,885 1,417 2 D 4,769 1,417 3 E 377 1,417 0 -- Total 14

Only fourteen out of sixteen seats have been allotted in this operation.

It is obvious that the quota is too large, and a smaller quota is ascertained in the following way. The number of votes for each list is divided by one more than the number of members already a.s.signed to such list, and the first seat still to be disposed of is allotted to that list which has the largest quotient. The following table shows the process:--

Lists. Votes. Quotient. Representatives.

A 5,537 4 1,384 4 B 9,507 7 1,358 6 C 3,885 3 1,295 2 D 4,769 4 1,192 3 E 377 1 377 0 -- Total 15

The largest quotient is 1384, and this figure, which is taken as the new quota, allows of the allotment of fifteen seats. There still remains one seat to be disposed of, and the process just described is again repeated, as shown in the following table:--

Lists. Votes. Quotient. Representatives.

A 5,537 5 1,107 4 B 9,507 7 1,358 7 C 3,885 3 1,295 2 D 4,769 4 1,192 3 E 377 1 377 0 -- 16

On this occasion all sixteen seats are allotted, the final quota being 1358.

The results obtained by the Hagenbach-Bischoff method are identical with those obtained by the d'Hondt rule. The operations required in the preceding example for the allotment of seats by the latter rule are as follows:--

List totals divided by A B C D E 1 5,537 9,507 3,885 4,769 377 2 2,768 4,753 1,942 2,384 -- 3 1,845 3,169 1,295 1,589 -- 4 1,384 2,376 971 1,192 -- 5 1,107 1,901 -- -- -- 6 -- 1,684 -- -- -- 7 -- 1,358 -- -- --

The sixteen highest quotients arranged in order of magnitude are:--

9,507 (List B) 2,376 (List B) 5,537 (List A) 1,942 (List C) 4,769 (List D) 1,901 (List B) 4,753 (List B) 1,845 (List A) 3,885 (List C) 1,589 (List D) 3,169 (List B) 1,584 (List B) 2,768 (List A) 1,384 (List A) 2,384 (List D) 1,358 (List B)

The lowest of these sixteen figures, viz. 1358, is the electoral quotient, and agrees with the final quota furnished by the Hagenbach-Bischoff rule. _Law for Elections to the Grand Council, on the principle of Proportional Representation, 26 January 1905_

1. Nomination papers for the various electoral districts must be handed in to the police department not later than three weeks before the day fixed for the re-election of the Grand Council.

They may contain the names of one or more persons eligible for election, provided that the total number of names in any nomination paper is not greater than the number of members which the electoral district in question is ent.i.tled to elect; any name may appear more than once, but not more than three times.

2. Nomination papers for town districts must be signed by at least ten qualified electors; those for country districts by at least three. An elector may sign one, and only one, nomination paper, on each occasion, in each electoral district.

When handing in the nomination paper the signatories thereto must designate one of their number to attend to any necessary formalities with the police department in connexion therewith.

3. The police department shall at once communicate with the candidates nominated, and call upon them to declare within two days whether they accept the candidature or not.

If the person nominated declines to stand for election his nomination shall be cancelled.

4. No candidate may appear on more than one nomination paper. If therefore any candidate be nominated in different electoral districts, or on several nomination papers in the same district, the police department shall, in informing him of the nominations, call upon him to declare, within two days, under which nomination he wishes to stand, and on receipt of his declaration shall strike his name off the other nomination papers.

If the candidate makes no declaration within the time fixed, the police department shall decide by lot under which nomination he shall stand.

5. The police department shall inform the representatives of the nominators of the cancellings due to the refusal of the nominees to accept nomination, or to the latter having been nominated more than once, and shall allow the former a period of two days in which to make further nominations. To these further nominations the declaration in writing of the person nominated, accepting the candidature, must be attached.

If this declaration is not attached, or if the proposed candidate already appears on another nomination, the supplementary nomination shall be rejected.

6. The final (definitive) nomination papers thus obtained shall be called lists, and no further alterations may be made in them. The lists shall each be printed on a separate sheet with the names of the candidates in the order in which they appear on the nomination papers.

The lists shall also be provided with a number (in rotation) for each electoral district, and if the proposers have given them any t.i.tles these shall likewise be printed.

If more than one list have the same t.i.tle the police department shall require the representatives of the nominators to make some distinction between them. If this is not done within two days, these lists shall be distinguished by further special numbers (in rotation).

The different lists shall be printed on paper of the same size and the same colour.

7. At least three days before the election these lists shall be delivered to each elector in an envelope, which shall at the same time serve as a voucher of the elector's right to vote. In addition to the printed lists, each voter shall receive a blank list containing no names, but as many numbered lines as there are members to be elected (free lists).

The voucher shall take the place of the present admittance card.

8. Electors must present themselves in person at the polling booth and deliver the voucher to the polling officers.

The latter shall retain the voucher, and in return give the elector an official stamp.

9. Each elector shall have as many votes as there are members of the Grand Council to be elected in his district, and shall for that purpose choose _one_ of the lists supplied to him. If he makes use of a printed list he may strike out any names and insert any others. Every vote is valid where the name of an eligible candidate is clearly given, and the only restrictions are that the same name may not appear more than three times, and that the total number of names may not exceed the number of members to be elected.

The voter may make the alterations he desires in the printed list selected by him, or fill in the free list either at the polling booth or before reaching it.

The voter shall affix the official stamp supplied to him to the list he has selected, and place the latter in the ballot box.

10. At the close of the poll the presiding officer shall open the ballot box and compare the number of voting papers therein with the number of vouchers received and the number of official stamps issued.

Only the official voting papers with stamps attached shall be valid.

11. The polling officers shall then examine the valid voting papers and ascertain by entering the votes on counting sheets how many votes each name has received.

If a voting paper contain more names than there are Councillors to be elected for the electoral district, then the votes in excess at the bottom of the list shall not be counted.

If a voting paper contain fewer names than there are Councillors to be elected in the district, then the number of votes not used shall be ascertained and shall be added (as list votes) to the list chosen by the elector, provided the latter has made use of a printed list.

The number of votes for each list shall then be ascertained by adding together the list votes and the vote given for individual candidates on the list.

If eligible persons not standing on any list receive votes, each of these names shall be treated as a separate list.

12. If no nominations have been handed in, those persons shall be elected who receive most votes.