First off, it may be useful to go back and take a look at this earlier question of yours and the answer to it. The concept of hard and soft electrophiles and nucleophiles was discussed. Basically, it was said that
hard nucleophiles are generally small, highly charged atoms. Because
of this they tend to be more reactive. They prefer to react with
similar (hard) electrophiles. Their reactions are usually kinetically
controlled with early transition states and are governed by
electrostatic interactions. Soft nucleophiles are generally larger
systems with a more diffuse charge. Because of this they tend to be
less reactive (more discriminating). They prefer to react with similar
(soft) electrophiles
The "take away" is that a hard electrophile prefers to react with a hard nucleophile while a soft electrophile prefers to react with a soft nucleophile.
Let's examine the system at hand, the nucleophile is the hydroperoxide anion ($\ce{HOO^{-}}$). You can draw two resonance structures to describe the anion, delocalizing the negative charge over both oxygens.
$$\ce{H-O-O^{-} <-> H^{+}~ [O-O]^{-2}}$$
Therefore, this anion is a softer nucleophile than $\ce{HO^{-}}$
The carbonyl group is a hard electrophile, while an $\ce{\alpha,\beta}$ unsaturated carbonyl, where the electron density is distributed over 4 atoms is a softer electrophile.
Soft reacts with soft, so would you expect the soft hydroperoxide anion to preferrentially react with a hard (carbonyl; 1,2 addition) or soft ($\ce{\alpha,\beta}$ unsaturated carbonyl; 1,4 addition) electrophile?