Problem with understanding Multi-party secure stable matching circuit

[zak100]

I am reading the following paper:

[SIZE=24pt]MPCircuits: Optimized Circuit Generation for Secure Multi-Party Computation[/SIZE]

https://eprint.iacr.org/2019/275.pdf

I have following questions:

1.     why Preference of group1 starts from L_0 where as preference list from group2 starts with L_(n/2+1)?

2.     Any reason why they used the priority encoder?

3.     What is the technique for the security of preference list?

Somebody please guide me. Zulfi.