Final answer:
Without the actual preference ballots, it is impossible to determine how many first-place votes Arthur has; a provided preference table would be required to calculate that information.
Step-by-step explanation:
The question does not provide the actual preference ballots to construct a preference table or determine the number of first-place votes for each candidate. However, in a situation where a preference table has been given with preference ballots, the number of first-place votes for a candidate such as Arthur would be the count of how many ballots have Arthur listed as the top choice. Without the specific data, it's impossible to answer how many first-place votes Arthur has. Therefore, I must refrain from guessing.
The problem described touches upon the concept known as a voting cycle or Condorcet paradox, which occurs when there are multiple choices, and the preference of the majority for one does not transitively apply to all other choices. This can result in an intransitive loop of preferences, making it challenging to determine the most preferred option by majority rule when more than two choices exist.