= Solution
The trivalent dopant is comparable in radius to Na$^+$ and is naturally accommodated on a sodium site rather than a chloride site. One charge-balanced incorporation reaction is
$$
\boxed{\mathrm{YCl_3\longrightarrow
Y_{Na}^{\bullet\bullet}+2V_{Na}'+3Cl_{Cl}^{\times}}.}
$$
Three cation sites are filled by one Y ion and two vacancies; the three chloride ions occupy the corresponding anion sites. The effective $+2$ substitutional charge is balanced by two singly negative sodium vacancies.
\b[YCl$_3$ doping primarily increases sodium-vacancy-mediated ionic conductivity], provided the vacancies remain mobile rather than strongly bound to the dopant. In contrast, sodium-rich doping introduces <electrons> and anion vacancies or interstitial-related defects. Neither mechanism requires holes as its compensating carrier, and an increase in vacancy number need not translate proportionally into conductivity if defect association reduces mobility.
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