Preserving Indexed comparisons between two list

Question

I have a list:

{{Subscript[i,  1], Subscript[a,  1], Subscript[b,  1]},
 {Subscript[i,  1], Subscript[a,  2], Subscript[b,  2]},
 ...,
 {Subscript[i,  r], Subscript[b,  1], Subscript[a,  1]},
 ...,
 {Subscript[i,  s], Subscript[b,  2], Subscript[a,  2]},
 ...,
 {Subscript[i,  n], Subscript[a,  n], Subscript[b,  n]}
}

in other words; this is a list indexed by:

{Subscript[i, 1], Subscript[i, 2], ..., Subscript[i, n]}

and every now and then; there are instances in the list where: {Subscript[a, i], Subscript[b, i]} is considered the same as: {Subscript[b, i], Subscript[a, i]}.

For example; if two jobs contained in the above list; namely,

{"Bill and Account Collectors", "Ticket Agents and Travel Clerks"}

have a job relational score of 0.5; then

{"Ticket Agents and Travel Clerks", "Bill and Account Collectors"}

also have the same relational score.

My question is; how can I collapse the above list to get a new list so that; if

{Subscript[a, i], Subscript[b, i]} == {Subscript[b, i], Subscript[a, i]}

then only

{Subscript[i, s], {Subscript[a, i], Subscript[b, i]}}

is included in my new list; and if:

{Subscript[a, k], Subscript[b, k]} not equal {Subscript[b, k], Subscript[a, k]}

then both:

{Subscript[i, s], {Subscript[a, k], Subscript[b, k]}}

and

{Subscript[i, t], {Subscript[a, k], Subscript[b, k]}}

are also included in my new list?

As an example, if

IndexedSOCList = {{1., 431011., 431011.}, {2., 431011., 433011.}, {3., 433011., 431011.},
   {4., 431011., 433021.}, {5., 433021., 431011.}, {6., 431011., 433031.},
   {7., 433031., 431011.}, {8., 431011., 433051.}, {9., 433051., 431011.},
   {10., 431011., 433061.}, {11., 433061., 431011.}, {12., 431011., 433071.},
   {13., 433071., 431011.}, {14., 431011., 434011.}, {15., 434011., 431011.},
   {16., 431011., 434031.}, {17., 434031., 431011.}, {18., 431011., 434041.},
   {19., 434041., 431011.}};

then the desired output is

(* {{1., 431011., 431011.}, {2., 431011., 433011.}, {4., 431011., 433021.},
    {6., 431011., 433031.}, {8., 431011., 433051.}, {10., 431011., 433061.},
    {12., 431011., 433071.}, {14., 431011., 434011.}, {16., 431011., 434031.},
    {18., 431011., 434041.}} *)

Answer 1

We use Union with a custom SameTest:

Union[IndexedSOCList, SameTest -> (Sort[#1[[2 ;; 3]]] === Sort[#2[[2 ;; 3]]] &)]

Alternatively, use DeleteDuplicatesBy:

DeleteDuplicatesBy[IndexedSOCList, Sort[#[[2 ;; 3]]] &]