Ranked choice preference with ties - Arrow's Impossibility Theorem
Allowing indifference will not solve the problem of the effect of the independence of irrelevant alternatives (combined with the unanimity and transitivity requirements).
You have said $b &gt;_1 c$ and $c &gt;_2 b$ should lead to $b =_s c$
Now consider  $a &gt;_1 b$ and $a &gt;_2 b$, which should lead to  $a &gt;_s b$ by unanimity

so $a &gt;_1 b &gt;_1 c$ and $c &gt;_2 a &gt;_2 b$ should lead to  $a &gt;_s b =_s c$ by transitivity
and thus $a &gt;_1  c$ and $c &gt;_2 a $ should lead to   $a &gt;_s c$ by the independence of irrelevant alternatives

And also consider  $c &gt;_1 a$ and $c &gt;_2 a$, which should lead to  $c &gt;_s a$

so $b &gt;_1 c &gt;_1 a$ and $c &gt;_2 a &gt;_2 b$ should lead to   $b =_s c &gt;_s a$
and thus $b &gt;_1  a$ and $a &gt;_2 b $ should lead to   $b &gt;_s a$

Combining these means $b &gt;_1 a &gt;_1 c$ and $c &gt;_2 a &gt;_2 b$ should lead to $b &gt;_s a &gt;_s c$

but that implies $b &gt;_1 c$ and $c &gt;_2  b$ should lead to $b &gt;_s  c$

inconsistent with your $b &gt;_1 c$ and $c &gt;_2 b$ leading to $b =_s c$