The doctrine of election (predestination) is tied tightly to other aspects of Reformed theology. Geerhardus Vos expresses this well in his Reformed Dogmatics (recently published in English for the first time thanks to Logos and Lexham Press – see here and here). Vos asks this question (in vol. 1.5.4): “At what points is the doctrine of predestination or election related to the rest of Reformed doctrine as a whole?” Here’s his answer (summarized):
1) It is a direct consequence of God’s sovereignty, as that has been shaped based on Scripture. Luther came to predestination from man and his salvation. Calvin did so from God. God is everything and the creature is nothing, and the creature, even in its highest importance, remains subordinate to God and must serve him. Whoever gives up the doctrine of predestination must therefore also drop the doctrine of the sovereignty of God and subsequently falsify biblical teaching at numerous places.
2) The doctrine of human inability after the fall is inseparably connected with predestination, so that one must maintain them both together or drop them both together. One of the two; it depends on God or it depends on man who will be saved. If one chooses the first, then one has accepted predestination.
3) Predestination is related to mystical union and the body of Christ. The elect form a body. In a body the members must be fitted to each other and are intended for each other. If this body of Christ originated accidentally by the free-will choice of individual men, then there would be no guarantee that it would become a properly proportioned body. God must decide in advance how many ought to belong to it, who those many shall be, and when they should be fitted into it. Predestination is nothing other than the decision of God concerning these matters.
4) Predestination is no less related to the doctrine of the merits of Christ. Christ earned for us 1) satisfaction of our debt of guilt by his passive obedience, 2) eternal life by his active obedience. According to Scripture, the Holy Spirit applies the merits of Christ to his people. If man himself decides by not believing or believing of himself, then faith is a work of man and no longer a fruit of the merits of Christ. Christ cannot have merited for us what we ourselves provide. And so it is, not only with faith but with all other parts of this application of salvation. Denial of predestination includes, so viewed, a denial of the actual merits of the Mediator.
5) Predestination also relates to the doctrine of the perseverance of the saints. God, by sovereign election, decides both the coming into the state of grace and the preserving of those who have once come into it.
Vos does say a bit more about these points – and they are worth reading for sure! The full discussion is found in volume 1 of his Reformed Dogmatics.