The Shulchan Arukh (Y.D. 321:6) rules that when a person performs the mitzva of pidyon peter chamor – redeeming his firstborn donkey by paying a sheep to a kohen – he recites the berakha, “Barukh Ata…asher kideshanu be-mitzvotav ve-tzivanu al pidyon peter chamor.” Interestingly, however, the Shulchan Arukh makes no mention of the recitation of a berakha in the context of arifa – the requirement for the owner to kill the firstborn donkey if he refuses to pay a sheep for its redemption. It appears that a berakha is recited over when one chooses the preferred option – paying a sheep to a kohen – but not if one chooses the option of arifa, killing the firstborn donkey.
This distinction was noted by the Minchat Chinukh (23), who writes that indeed, mitzvot which are observed as a less preferred option do not warrant a berakha. The Sages instituted berakhot before performing what the Minchat Chinukh calls “mitzvot chavivot” (“beloved” or “cherished” mitzvot), to the exclusion of mitzvot which one performs only because he chooses against the preferred mode of action. As a precedent for this theory, the Minchat Chinukh cites sources that a man performing the mitzva of yibum – marrying his deceased brother’s widow, after the brother died without children – recites a berakha, but a berakha is not recited over chalitza – the ceremony performed if the brother refuses to marry the widow. Since chalitza is performed only as a second option, and is not the preferred mode of action in this situation, it does not warrant a berakha. (It should be noted that nowadays we do not perform yibum, and chalitza is done in all situations where a husband dies without children and has a brother, but in principle, yibum is the preferred option.) By the same token, the Minchat Chinukh writes, one recites a berakha over the mitzva of redeeming a firstborn donkey, but not if he refuses to redeem the animal and chooses to kill it, instead.
Rav Shemuel Yitzchak Hillman, in his Or Ha-yashar commentary to Masekhet Bekhorot (11a), questions the Minchat Chinukh’s reasoning, noting that once one refuses to perform the preferred mitzva, he now bears a full-fledged mitzva to perform the alternative. The consensus among the halakhic authorities, following the view of the Rambam, is that arifa constitutes a mitzva, even if it represents the less preferable option. Its less preferred status, seemingly, should not affect the requirement of a berakha, as once the owner has made the decision not to redeem the donkey, he bears an obligation to kill it, and this mitzva should warrant a berakha like other mitzvot.
Rav Hillman therefore suggests explaining this halakha on the basis of a famous responsum of the Rashba (1:18) concerning the general topic of berakhot recited over mitzvot. The Rashba addresses the question of why Chazal enacted the recitation of a berakha over certain mitzvot but not others, and amidst his discussion he establishes that a berakha is not recited over a mitzva whose completion is uncertain. For example, we do not recite a berakha before giving charity, because the possibility exists that the recipient will refuse the donation. Since the effect is not definite, no berakha is recited. This rule, Rav Hillman suggests, should apply to arifa, as well, and all the more so. Since the Torah itself prefers that the owner perform the mitzva of redeeming the animal, this option hovers over the individual up until the moment when the act of arifa is completed. Rav Hillman reasons that if an external possibility – such as a pauper refusing a gift – suffices to negate the propriety of a berakha, then certainly this is true of a possibility which the Torah wants the individual to choose. Since the Torah prefers redeeming the animal over killing it, the option of arifa is regarded as “indefinite” even after the owner made a firm decision not to redeem it. (Likewise, the option of chalitza is treated as “indefinite” given the preferred option of yibum.)