Imagine that you are one of three judges for a singing competition. You need to decide which of three finalists should win. You have no qualifications to evaluate actual singing ability, so you plan to make your choice based entirely on your preferences for the style of music that each performer chose: a sappy ballad, a traditional Irish folk song, and a heavy metal song. Luckily for you, you happened to see the notes written by the other judges, and so you know how your fellow judges ranked the finalists. One judge had the following preference ordering: ballad > Irish folk song > heavy metal. The other judge had the following preference ordering: heavy metal > ballad > Irish folk song. Your preference ordering, however, is the following: Irish folk song > heavy metal > ballad. The rules of the competition do not specify how the judges are to reach their decision.
1) Let’s suppose that you suggest a round-robin tournament in which everyone votes on the finalists in a series of pair-wise contests. How many pair-wise contests does each of the finalists win? Is there a Condorcet winner? Explain. Does this decision-making process identify a clear winner? Explain.
2) Now let’s suppose that you propose a decision-making procedure by which all of the judges begin by considering only a subset of the available pair-wise contests. The specific decision-making procedure that you propose is that two finalists should compete in a pair-wise contest with the winner competing in a second and final round against the remaining finalist. Given your preference ordering, which finalist do you want to win? If you were in charge of setting the voting agenda and could determine the order in which the pair-wise contests took place, what order would you pick and why?
The main indications of this class were initially, and normally, extraordinary and interesting in its authentic, uprooted setting, extending right to AD 1000, when the thought previously happened of joining a few voices to sing a tune; it was the point at which the Church, who were really the most fundamental effect and impact on the improvement of music in those occasions, saw a need to organize the single-line unaccompanied serenades, because of how they had been used for a serious long time in sacrosanct customs. Regardless, for what reason would the congregation place worry in music? What was their view on music, when all is said in done?
The appropriate response lies in the historical backdrop of the early Christian church itself; the congregation was, before, a little yet decided gathering who had confidence in the ‘mission’ of changing over Europe into Christianity. In this manner, they profoundly attempted in the assignment to impact and avoid the way of life of the Pagan culture at that point, which was altogether supported by the utilization of a “medium” that would go about as a channel to spread Christian convictions: Music.
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Music, or all the more explicitly Western Art Music, filled in as an incredible mode for the Early Christians, as it was seen as one of the “most grounded and natural powers of nature which had the ability to influence human idea and mind.”(Greek reasoning) Moreover, this view was likewise absorbed with the way of life and conventions of the congregation, in which, as should be obvious, how Christian serenades were gotten from, in any case.
This gives us how they started to see music as a key idea, at the same time, whenever looked from another point of view, with no acknowledged composed framework to signify the pitch or length of a note, the scoring of music was unavoidably a disputable issue. Consequently, a Benedictine cleric named Guido d’Arezzo, whose life as a melodic researcher accommodatingly orchestrated with the Church’s necessity for melodic unification, is, when all is said in done, credited with the presentation of a fight of flat lines, by which one could precisely record the pitch of notes, subsequently starting the primary idea of composed workmanship music.