Synthesized answer
Elective kingdoms are not sovereign because the elective king is considered a minister of the sovereign, not a sovereign themselves [1]. They have sovereign power put into their hands for a time [1]. If an elective king has no power to appoint his successor, then the sovereignty rests with another person or assembly who can elect a new king [2]. This indicates that the sovereignty was in them before, as no one has the right to give what they do not possess [2].
Furthermore, if the elective king's power is limited, he is not superior to those who have the power to limit him, and therefore not supreme or sovereign [3]. The sovereignty, in such cases, resides in the assembly that has the right to limit him [3]. While elective kings hold power in use, they do not possess the sovereign power in their own right [4]. The right to dispose of succession, in the case of an elective monarch, may belong to the dissolved multitude [4].
Synthesized from the book passages below. Chat with the book on Feynman for follow-up.
From the book
reduce them to three, and may thereby be inclined to think there be other Formes, arising from these mingled together. As for example, Elective Kingdomes; where Kings have the Soveraigne Power put into their hands for a time; of Kingdomes, wherein the King hath a power limited: which Governments, are nevertheless by most Writers called Monarchie. Likewise if a Popular, or Aristocraticall Common-wealth, subdue an Enemies Countrie, and govern the same, by a President, Procurator, or other Magistrate; this may seeme perhaps at first sight, to be a Democraticall, or Aristocraticall…
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…
e: For none have right to give that which they have not right to possesse, and keep to themselves, if they think good. But if there be none that can give the Soveraigntie, after the decease of him that was first elected; then has he power, nay he is obliged by the Law of Nature, to provide, by establishing his Successor, to keep those that had trusted him with the Government, from relapsing into the miserable condition of Civill warre. And consequently he was, when elected, a Soveraign absolute. Secondly, that King whose power is limited, is not superiour to him, or them that have the…
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…
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…