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To add to MAGolding's answer, Murad II may have been willing to arbitrate because it gave him influence over the internal politics of the shrunken and weakened Byzantine Empire.
Constantine XI Palaiologos and The Empress Helena favoured union between the Eastern Orthodox Church and the Roman Catholic Church. They hoped that this would bring them support from Catholic Europe, which had demonstrated it was stronger than the Byzantine Empire, by taking Constantinople in 1204.
However, the Byzantine population steadfastly opposed the union of the churches. Demetrios Palaiologos, Constantine's rival for the throne, was opposed to that union, which gave him popular support. Murad II decided the dispute in favour of the candidate with less popular support, improving his empire's chances of conquering Constantinople, which happened only four years later.
The expression "Byzantine Politics" describes this kind of behaviour.
Upvote:6
because it is normal for participants in a succession dispute to ask for foreign help, thus often getting foreign warriors involved in a civil war. Thus Byzantine civil wars in earlier times had often resulted in Turkish, Serbian, Bulgarian, Venetian, or Genoese military and naval involvement.
It is also common to ask for foreign arbitration. Usually a more powerful foreign realm is asked to arbitrate. Ottoman Sultan Murad II was much more powerful than what little as left of the Byzantine empire. The capital of the Ottoman Empire was then Edirne/Adrianople, which was much closer to Constantinople than any other foreign capital making communication quicker.
Thus Ottoman Sultan Murad II was a fairly logical choice to ask to arbitrate.