Facebook – How to make anonymous poll in a whatsapp group, facebook group, or google group

I am a member of mensa Indonesia. I was tasked to do an election to select the next Indonesian's mensa's fuhrer.

Like all normal elections, the polls need to be secret to avoid bloodshed and civil wars. Also, each member can vote only once. Only members in good standing can vote.

The plan is to put all such members in a group. Whatsapp group or facebook group.

Then uses a third party app to get all members in the group to vote.

Then tada, we got a new supreme leader for the next 2 years.

Facebooks allow polls but it isn't anonymous. Whatsapp doesn't have poll.

Are there any third party apps or robots that allow those things?

It doesn't have to be whatsapp group, or facebook group, or google group. It can be telegram group or any group.

1. We get people in a group.
2. We vet that only the good guys are in the group.
3. We get them to vote.

That's the plan.

Let me give you a sample solution that DOESN'T fit my criteria

I do not think whathash is suitable for his purpose

1. Anyone that got the message can vote, even those that are not member of mensa
2. People with different phones and whatsapp account can vote several times.
3. Not ideal because someone, namely me, can see who vote for what. This one can be relaxed. Basically I want that info to be hidden from all people, if possible, even from those conducting the poll.

I WANT DIFFERENT SOLUTIONS

I want everyone go join my group. Then only people in that group can vote

Facebook polls actually works almost perfectly. However, I need a way to prevent anyone from seeing who vote for who. We need to minimize bloodshed here. While there is no way voting for mensa leaders can lead to any kind of bloodshed, we want to generalize the system to more politically sensitive votings.