Synthesized answer
If an elective king has no power to appoint his successor, then either there is another known man or assembly that can elect a new king after his death, or the commonwealth dies and dissolves with him [3]. In the latter case, the commonwealth returns to a state of war [3].
If the right to appoint a successor is not with the current possessor, it returns to the dissolved multitude [1, 2]. This means the commonwealth is dissolved, and the right to sovereignty belongs to whoever can acquire it [5]. This outcome contradicts the original intent of establishing the commonwealth for perpetual security [5].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
that is in possession, has right to dispose of the Succession, or else that right is again in the dissolved Multitude. For the death of him that hath the Soveraign power in propriety, leaves the Multitude without any Soveraign at all; that is, without any Representative in whom they should be united, and be capable of doing any one action at all: And therefore they are incapable of Election of any new Monarch; every man having equall right to submit himselfe to such as he thinks best able to protect him, or if he can, protect himselfe by his owne sword; which is a returne to…
y their Authority, that the Election is made; and by the same it may (when the publique shall require it) be recalled. The Present Monarch Hath Right To Dispose Of The Succession The greatest difficultie about the right of Succession, is in Monarchy: And the difficulty ariseth from this, that at first sight, it is not manifest who is to appoint the Successor; nor many times, who it is whom he hath appointed. For in both these cases, there is required a more exact ratiocination, than every man is accustomed to use. As to the question, who shall appoint the Successor, of a Monarch that…
Democracie, or Aristocracie of another Common-wealth, Democratically, or Aristocratically governed, but Monarchically. And first, concerning an Elective King, whose power is limited to his life, as it is in many places of Christendome at this day; or to certaine Yeares or Moneths, as the Dictators power amongst the Romans; If he have Right to appoint his Successor, he is no more Elective but Hereditary. But if he have no Power to elect his Successor, then there is some other Man, or Assembly known, which after his decease may elect a new, or else the Common-wealth dieth, and dissolveth…
inheritance of his power; it is determined by his expresse Words, and Testament; or by other tacite signes sufficient. Succession Passeth By Expresse Words; By expresse Words, or Testament, when it is declared by him in his life time, viva voce, or by Writing; as the first Emperours of Rome declared who should be their Heires. For the word Heire does not of it selfe imply the Children, or nearest Kindred of a man; but whomsoever a man shall any way declare, he would have to succeed him in his Estate. If therefore a Monarch declare expresly, that such a man shall be his Heire, either…
s in a person subject, and may be assumed by the Soveraign at his pleasure; and consequently the Right is in himselfe. And if it be in no particular man, but left to a new choyce; then is the Common-wealth dissolved; and the Right is in him that can get it; contrary to the intention of them that did institute the Common-wealth, for their perpetuall, and not temporary security. In a Democracy, the whole Assembly cannot faile, unlesse the Multitude that are to be governed faile. And therefore questions of the right of Succession, have in that forme of Government no place at all. In an…