Bianconi-Barabasi Dancing Contest

A group of friends goes to a club to participate in the Bianconi-Barabási Dancing Contest, where they compete to see who can attract the most dance partners throughout the night. Each friend has a different combination of dancing experience (how many times they've danced in their lives) and breath quality (which influences how socially attractive they are). In this scenario, breath quality represents fitness (social attractiveness), and dancing experience represents degree (how many times they've danced before). Here are their attributes:

  • Friend 1 (Professional dancer with bad breath):
    • Dancing experience (degree): 9/10
    • Breath quality (fitness): 2/10
  • Friend 2 (Amateur dancer with the best breath in town):
    • Dancing experience (degree): 3/10
    • Breath quality (fitness): 10/10
  • Friend 3 (Medium dancer with average breath):
    • Dancing experience (degree): 6/10
    • Breath quality (fitness): 6/10
  • Friend 4 (Medium dancer with average breath):
    • Dancing experience (degree): 5/10
    • Breath quality (fitness): 5/10

At the start of the party, who is most likely to attract a partner for the first dance of the night?
After infinite dances, considering that the night never ends, and everyone has infinite chances to ask for partners to dance, who will end up with the most dance partners?

A) Friend 2 has the most chance to get the first dance of the night, and Friend 1 will have more dances by the end. 

B) Friend 1 has the most chance to get the first dance of the night, and Friend 2 will have more dances by the end. 

C) Friend 3 has the most chance to get the first dance of the night, and Friend 4 will have more dances by the end.

D) Friend 3 has the most chance to get the first dance of the night, and Friend 2 will have more dances by the end. 

E) None of the above.

Original idea by: João Vitor Baptista Moreira

Comentários

  1. Joao Meidanis14 de outubro de 2024 às 16:31

    Nice question, but, to be able to draw conclusions similar to the Bianconi-Barabasi model, we need a setting where at each time step there are only m dances, with the same new dancer, who will choose these m partners with probability proportional to the product of experience and breadth quality, with the latter remaining constant throughout the contest and the former increasing by one for each partner when they dance.

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