verb form of tiebreakers?

Tip the scales is commonly used with this meaning.

Cambridge Dictionary

tip the balance/scales (also tilt the balance)

If something tips the balance or tips the scales, it is the thing that causes a particular situation to happen or a particular decision to be made, when other situations or decisions are possible:

The teams were evenly matched until two quick goals from Rooney tipped the balance in favour of England.

She was a good candidate, but her lack of computer skills tipped the scales against her.

In the example sentence,

I have a lot of options to solve this problem, and what tips the scales for me is simplicity.

Break the ties is fine, although it’s often used in sports contests where there are only two opponents; thus, break the tie.

I’d recast, and say “I use simplicity to choose between them.”