Hasta donde te entendi... se me ocurre esto...
Código HTML:
<form name="formulario" method="post" action="">
<select name="s1" onChange="document.formulario.s2.value=0; document.formulario.s3.value=0;" >
<option value="0">NO ASIGNADO</option>
<option value="a">Persona A</option>
<option value="b">Persona B</option>
<option value="c">Persona C</option>
</select>
<select name="s2" onChange="document.formulario.s1.value=0; document.formulario.s3.value=0;">
<option value="0">NO ASIGNADO</option>
<option value="a">Persona A</option>
<option value="b">Persona B</option>
<option value="c">Persona C</option>
</select>
<select name="s3" onChange="document.formulario.s1.value=0; document.formulario.s2.value=0;">
<option value="0">NO ASIGNADO</option>
<option value="a">Persona A</option>
<option value="b">Persona B</option>
<option value="c">Persona C</option>
</select>
</form>