A VIE is that in which the total equity investment is less than the expected loss, as described by Jim Mountain of Deloitte & Touche.
As the rules are written, if the entity is deemed a VIE, any one party that holds the majority of the expected loss will consolidate. If no one party holds the majority of the expected loss, than the party that holds the majority of the expected residual return will consolidate. If no party owns the majority of either the EL or the ERR, no one consolidates.
For CDOs, strategists will make the case that there is substantive equity investment (which is greater than the expected loss), leading to a "voting rights" interpretation. Here, the equity holders in the CDO could be given more powers, such as the right to replace the collateral manager at any time (as a board of directors to a company can replace its senior management).