I'll keep this simplistic.
Why is it different if each man has two witnesses vs one witness.
Regardless they are Machrishim Zeh et Zeh 1. In terms of which one of them is the slave and which one is the husband & in terms of who the owner of the Chavilah is. If they are machrishim they negate each other. A negative & a Positive gives Zero. She doesn't have witnesses that were proven or disproven.
So I understand the Answer that she doesn't require a get unless she wants the chavilah- but even that is difficult to understand. There is a double claim going on each man is claiming ishus and ownership over the chavilah and over the other being their Karka!
She claims they are Both her slave and it's her chavilah
At first glance this appears to be more of a mamonos question ergo with all three it should be "Hamotzi Meichaveiro Alav HaRaayah"?
Why would her receiving two gittin that she insists she doesn't require entitle to the chavalis as Kesubah compensation?
That leads to a myriad of questions- we don't know the conditions of the kesuvah- so why would two gittin entitle her to a chavalis? Also if the Chavalis is actually hers and she's marries to one of them what do the gittin accomplish etc....
Avraom, United States
1) As to your question that the witnesses cancel each other out|: The Rishonim ask the question and give several answers:
a. The Raavad (et al)says that there is technically no contradiction because she may have been married and divorced from man #1 and then afterward married to man #2; this leaves the testimony that these men are not Avadim intact
b. The Rashbo says that although there is a contradiction regarding to whom she is married, there is no contradiction to the fact that she is a married woman (and consequently the men are not her slaves)
c. The Rosh explains that the Gemora means to say that there are witnesses "to this one OR to that one"
2) Yes, indeed this is a Mammonos question and one of the major dynamics at play is "HaMoitzi Meichveiro Olov Hara'ayo".
3) About the question why she should get a Kesuva that she says is not coming to her: I was also botherd by that question when I learned the Sugia, and I think the correct understanding is like this: In effect, she never gets "Kesuva" but rather she gets the "Chavila" that she has consistently demanded for herself. Just, she has no proper proof of her ownership rights in the "Chavila". Nonetheless, when each man willingly gives her a Get, this is tantamount to each one making a Hoda'as Ba'al Din that they owe her the Kesuva, and this translates into a real monetary debt. She can collect that debt from the Chavila even though they are paying Kesuva and she is collecting her package. This is what Rashis says at the end of D"H Tzricha Shnei Gittin.
4) We don't need to know the details of her Kesuva; the standard universal Kesuva is the income required to live for one year; we assume that it is unlikely that the Chavila is worth more than that (and even if it is she will receive proportionately what she has coming to her which is enough for the needs of understanding the Sugia)
5) As to the question, "what do the Gittin accomplish": Since they give the Gittin willingly, they become obligated to pay her the Kesuva.
6) I hope that covers the major bases, please feel free to send a follow-up question if you like.
Shimon Brodie