Before jurors decide whether a convicted killer should live or die, should they be told about the character of the victim and the impact of the murder on society?

That's what the U.S. Supreme Court was asked this week to decide in a potentially historic case that could test its wisdom to the limit.In a rare appearance before the high court, U.S. Attorney General Dick Thornburgh urged the justices to scrap earlier precedents, declare such "victim-impact" statements constitutional, and let Congress and the state legislatures write the rules for courtrooms.

The Supreme Court ruled in 1987 and 1989, both times by 5-4 margins, that victim-impact evidence is so emotional and inflammatory that it "creates a constitutionally unacceptable risk that the jury may impose the death penalty in an arbitrary and capricious manner."

Since then, the court has become more conservative. The very fact that a new case on the issue came before the Supreme Court this week indicates that the panel's current majority dislikes the precedents that Thornburgh wants overturned.

But at Wednesday's hearing, two of the five justices who have been dissatisfied with earlier rulings on victim-impact evidence asked questions that seemed particularly critical of Thornburgh's position. Consequently, the outcome of the current case, expected next June, is anything but certain. Besides, there's room for more than a little ambivalence on this issue.

On the one hand, it would be hard to let prosecutors laud the personal qualities of murder victims without letting defense attorneys attack them. Likewise, the more pointed such arguments become, the more difficult it may be for jurors to render an objective decision on whether a particular killer should live or die.

On the other hand, the fact is that society is hurt much more by some murders than by others. The killing of, say, a prominent community leader with children has more impact than the killing of a childless man who cheated on his income taxes and his wife.

More important, the present arrangement is flawed. Jurors commonly hear defense attorneys plead for mercy by praising the character of the convicted killer, tearfully describing his or her deprived childhood, and insisting that society rather than the person in the dock is to blame for the murder. But prosecutors are never allowed to describe a murder victim as a beloved person and a pillar of the community.

The result of this imbalance is that jurors may tend to think of the person awaiting sentence as a tangible individual but to consider the victim as an abstraction.

Somehow, juries need to be more deeply impressed with the fact that victims are not just faceless statistics. But it's much easier to prescribe this objective than it is to describe a method for achieving it without whipping courtrooms into an emotional lather.