G.M. looking for some advice and suggestions on how to resolve a spacific competition fairly. (Game not yet posted.)

Ok so the situation that I have written my self into is this. In my home brew campaign, that fortunately has not been posted or started yet, the PC's are competing in a series of tests of skill, strength, cunning and intellect VS other NPC parties and individual npc's in an effort to win the favor of wealthy npc sponsors. The explorers league has organized this competition in an effort to rais money for an expedition to a recently discovered and wholly unexplored island believed to be the lost land of the ancients. I could use some advice or suggestions on how to make keeping track of just how interested said wealthy sponsor are in the PC's vs how interested they are in other npc's . I want it to be fair but challenging. I think it would also be interesting if it were possible fore diferent players to gain the favor of different sponsors. But I am not quite sure how to approach this aspect of my campaign. I love the idea of letting my pc's show off and strut there stuff as it were in front of a crowd of Nobles some of whom may have more nefarious interests in the island than the pc's yet realize. I'm just not sure of the best and most fair way to track the interest of the various Wealthy sponsors, waiting to open up there wallets for there best possible investment prospects. Does any one have any thoughts?

look up performance combat from Pathfinder. Can find the rules for it in the SRD online. Will give the basis for gaining/losing favor of a fight

Good suggestion thank you.

id like to suggest a few tips if you are interested. 1- if you total the 'patron's" reaction to the party Vs the NPC (and not count it seperatly per individuals) then you can place a token of each patron on the map and use the first two bars (green and i belive blue circles when you click them) as the 'amount" of favor they have for each group. after each achivment or disapontment of the party\npc you can add or subtruct that value. this also allow you to have some of them marked as bios thowerd the characters or the npc as you see fit. and rolls of say diplomecu\bluff intimidate can change that value. (if you play D&D \pathfinder. ) or better yet let them RP it. 2- make a day by day hour by hour calender showing what test\events might change their favor. event like speaches\party\test\ skill performence and others. laeve room for more then one way one can impress a patron(or impress one and disapont an other). and decide ahead of time how the npc would try and react.(and if you have time and the party can't interact in the npc's job you can also roll for them ahead of time to save gaming time.) 3- let the party figure out how to aprouch each patron. deside their difrences and point of veiw and what they would like or dislike to see. and slip a few clues for the party(some of them migth be easy t ospot. like sucess vs feliure .some might be tactiacl opinioins or moral ideas. this can be a graet source for RP.

This is great. Using this and the above posted performance combat for an arena competition. as one of the "Tests" should give me exactly what I need. Thanks to both of you fore the in-put.

This is my gut advice but probably the least desired: Don't make up rules for the patron responses. Decide what will make the best story and let that follow accordingly. If the PC's are losing a lot but you feel the story requires them to have access to Patron A and B, then give them a different avenue to get the attention of those patrons. A side job hired on by patron C or to sabotage the favored party that Patron D is backing and whose defeat would please A and B. I guess from a story telling point of view I don't understand your goal with the "score" of the competition. If the PC's end up losing, does it mean the campaign stops? Or that they're sent off with less stuff than they should be/ would be?