It then follows that I am also entitled to the voting rights, as they have also sold the voting rights to me. Therefore, in turn, it also follows that the seller cannot exercise the vote for shares that they have sold - that right has transferred to me at the time of the trade, using the same logic.
You are only entitled to physically receive dividends from the company from the date that your name is entered on the share register. Likewise, you are only entitled to exercise voting rights from the date that your name is entered on the share register.
In the circumstance where your name is not on the share register in time you are NOT "entitled to THE dividend" (it's impossible for the company to pay the dividend to you because your name is not on the share register and the company don't know who you are yet). Instead you are entitled to a cash compensatory payment from the person who sold you the original shares.
This additional payment (a "manufactured dividend") is a specific contractual term between buyer and seller that specifies what happens if a dividend is paid to the wrong person. The specific standard contractual term for votes is that the buyer is entitled to exercise them from the date of settlement. If you're unhappy with the contract then you should attempt to negotiate something different BEFORE buying, especially if you think that it's important to you, there's little point trying to renegotiate a bargain AFTER it's been traded.