Merriam-Webster defines "could do worse" as an idiom:
used to say that a particular choice, action, etc., is not a bad one
You could do worse than to vote for her.
Although I would have gone with simply "vote" without "to" myself, I think it's still okay to add "to" after "could do worse than", as shown in M-W.
That said, I was wondering if using "voting" would be also correct here.
There's a 2011 thread showing this form:
...you could do worse than using a simple JScript application.
Where nobody seems to raise any question about the form "using."
And then here's a 2022 New York Times article adopting the form "adding":
There’s a character in Adam White’s debut novel, “The Midcoast,” who at one point starts to chafe against her small-town circumstances and decides to do something about it. “She went to the library,” White writes, “and started checking out every kind of book — romance novels, spy novels, biographies, memoirs, history books, cookbooks — anything in print.” That’s my kind of character, I thought when I reached that passage, and if it’s your kind of character too then you could do worse than adding “The Midcoast” (think “Ozark” meets “The Great Gatsby” in Maine) to your reading list this week.
Does this mean this -ing form is always natural after "could do worse than"?