It is well known that it takes three to be obligated in zimmun and that ten are required for a minyan, but how many are required to screw in a lightbulb?
To change a lightbulb, you need a crew that is superior in both number and wisdom to the crew that put the lightbulb there in the first place.
- Collective Bargaining Agreement of the International Brotherhood of Lighbulb-Changers II:3:b:iv, citing Rambam, Mamrim 2:2
We are not allowed to change the light bulb, but we can be mechadesh a new light bulb. However, in order to know whether the light bulb is being changed or whether the new one is a proper chiddush, one must have knowledge of the full range of Torah; knowing just the halachos of light bulbs is insufficient. In addition, the chiddush of a new light bulb must be from within the system, not from the outside. Psychologizing, historicizing, or otherwise rationalizing the previous light bulb's expiration is illegitimate.
Replacing a burnt-out lightbulb with one that works is a tiny act of tikkun olam, repairing the world. Not only is it repair but, being about light, it's a small repair to the original shattering of light, tzimtzum! Not only is there no minimum number of Jews to make this repair, but you are obligated to take the steps you can when you discover the problem. As Rabbi Tarfon teaches in Pirke Avot 2:16:
He used to say: It is not your responsibility to finish the work, but neither are you free to desist from it.
We keep using the broken lightbulb זכר לחורבן.
We learn about changing the lights from the service in the Bais HaMikdash. There, the Kohahim tended to the Ner Tamid, which was always burning. Only a Kohen could tend to the menorah, and likewise today only a Kohen can change a lightbulb. The procedure is that he comes in the morning and removes the old light that was burning all night. Then he comes back in the evening and puts in a new lightbulb. Today we cannot ask a Kohen to do work for us, and also we are not 100% sure on the mesorah for kohanim, so usually light bulbs remain unchanged.