Well, it could also mean that someone else who isn't a YC partner was rejected to let him in. Of course, I don't know whether or not that is the case, but this is where a conflict of interest could potentially arise from.
He was a YC partner. He no longer is. And there's a difference between an equity partner and other types of partners. But again, YC is incentivized to let in companies they believe will deliver the most total value to the YC portfolio, so admitting Luke at the expense of another founder who was better qualified is directly contrary to their interests. Also, the YC batch sizes aren't fixed, and they have wiggle room. To avoid the conflict, they could just admit one additional startup who would have otherwise been cut.
You are alleging bias, not a conflict of interest.
YC accepted into their program as a founder someone who was a partner. Does that really sound like bias to you? If a former professor at a university applied to be a grad student, would you accuse the university of a conflict of interest?
Firstly, other comments have disproven my claim already as I was under the assumption that YC accepted a fixed number of startups per batch.
> You are alleging bias, not a conflict of interest.
I'm not sure I understand the difference.
> YC accepted into their program as a founder someone who was a partner. Does that really sound like bias to you?
Yes, if and only if the decision resulted in another equally strong application being rejected, either directly or indirectly.
> If a former professor at a university applied to be a grad student, would you accuse the university of a conflict of interest?
Perhaps, because the committee that decides whether or not to accept a student consists of professors who likely know the former professor, which will likely introduce bias (positive or negative).
IIRC the exact number of startup that are founded is not fixed, they have some approximate idea but they found whatever they think is promising enough. So they didn't fill an slot in a fixed amount of startups.