Minimal number of supporters need to win a multi-level election

Question

On July 27th, Max Alekseyev posted a sequence to the OEIS:

A290323: Minimal number of supporters among total of n voters that may make (but not guarantee) their candidate win in a multi-level selection based on the majority vote at each level.

He gives the following example for $n=9$:

For n=9, four supporters are enough in the following 2-level selection with (s)upporters and (o)pponents: ((sso),(sso),(ooo)). On the other hand, no smaller number of supporters can lead to a win in any multi-level selection. Hence, $a(9)=4$.

The sequence begins:

1, 2, 2, 3, 3, 4, 4, 5, 4, 6, 6, 6, 7, 8, 6, 9, 9, 8, 10

A link (in Russian) from the OEIS sequence contains the following image:

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The sequence is intriguing to me, but I'm having some trouble making sense of it. (Plus, I can't read Russian and therefore cannot make sense of the links.) In particular, must all of the rounds have an equal number of voters? Are rounds allowed to end in ties?

I'm hoping someone can give more explicit rules for the sequence, and perhaps give some more examples.

Answer 1

The OEIS sequence links to this Russian paper, wherein the question is defined more clearly:

В стране Анчурии, где правит президент Мирафлорес, приблизилось время новых президентских выборов. В Анчурии 20 000 000 избирателей, из которых только один процент (армия Анчурии) поддерживает Мирафлореса. Он хочет быть демократически избранным. <Демократическим голосованием> Мирафлорес называет вот что: всех избирателей разбивают на несколько равных групп, затем каждую из этих групп вновь разбивают на некоторое количество равных групп, затем эти последние группы снова разбивают на равные группы и так далее; в самых мелких группах выбирают представителя группы — выборщика, затем выборщики выбирают представителей для голосования в ещё большей группе и так далее; наконец, представители самых больших групп выбирают президента. Мирафлорес сам делит избирателей на группы. Может ли он так организовать выборы, чтобы его избрали президентом? (При равенстве голосов побеждает оппозиция.)

Translation:

In the country of Anchuria, where President Miraflores rules, it is the time of new presidential election. In Anchuria, only one percent of the 20,000,000 voters support Miraflores, namely the army of Anchuria. He wants to be democratically elected. Miraflores demands: all voters be split into several equal groups, then each of these groups be again divided into a number of equal groups, and those last groups be again divided into equal groups and so on; in the smallest groups, select a representative of the group - the elector, then the electors choose representatives for voting in an even larger group and so on; finally, representatives of the largest groups choose the president. Miraflores himself divides voters into groups. Can he organize elections so that he is elected president? (With equality of votes, the opposition wins.)

(Disclaimer: I used Google Translate with some corrections by myself.)

Now, we can address your questions:

In particular, must all of the rounds have an equal number of voters?

Yes, but not necessarily with other rounds.

Are rounds allowed to end in ties?

Yes, in which case the opposition wins.