Yes. Equal voting systems have been thoroughly researched through election method simulation of various voting systems
. Approval voting in the first stage and a vote between the top two approved in the second stage is the highest-performing simple, unranked voting system. It also has a high propensity to elect the candidate that could beat all others one-on-one when such a candidate exists (the so-called Condorcet winner
In an analysis of 51 different voting methods, including Range, Approval, Bucklin, IRV, Top 2 Plurality and many more, Approval with a Top Two outperformed all but two (Range and Range with a Top Two - also equal voting methods), and far outperformed the system we use today. It is by far the best system that uses a simple two-stage balloting system like the one we use today.